Ch01 A Preview of Business Statistics

*P54282A0124*Turn over Instructions• Useblack ink or ball-point pen – pencil can only be used for graphs, charts, diagrams, etc.• Fill in the boxesat the top of this page with your name, candidate number, centre code and your candidate ID number.• Answerall questions.• Answer the questions in the spaces provided – there may be more space than you need.• Answers should be given to an appropriate degree of accuracy.Information• The total mark for this paper is 100.• The marks for each question are shown in brackets – use this as a guide as to how much time to spend on each question.• A formulae sheet is provided at the front of this question paper.• Calculators may be used.Advice• Read each question carefully before you start to answer it.• Try to answer every question.• You are advised to show your workings.• Check your answers if you have time at the end.Certificate in Business Statistics (VRQ)Level 2ASE20096Monday 20 November 2017Time: 2 hours 30 minutesComplete the details below in block capitals.Candidate nameCentre Code Candidate NumberCandidate ID NumberTotal MarksP54282A©2017 Pearson Education Ltd.1/1/1/1/1/1Paper ReferencePearson LCCIYou must have:HB pencil, eraser*P54282A0224*2*P54282A0324*Turn over3BLANK PAGE*P54282A0424*4Answer ALL questions. Write your answers in the spaces provided.1 AMG, a market gardening company, wishes to investigate the relationship betweenthe total weight of tomatoes produced by a tomato plant (y kilograms) and theamount of fertiliser used (x grams).An experiment was conducted by applying known amounts of fertiliser to similarplants and weighing the resulting yields.Here are the results obtained from 10 tomato plants.Weight of fertiliser (x grams)Yield of tomatoes (y kilograms)0 4.012 4.704 5.026 4.848 5.3810 5.6112 5.4714 5.8016 5.9018 5.95(a) State which of the two variables is the response variable.You must give a reason for your answer.(2) .................................................................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................................................................... ....................................................................................................................................................................................................................................................................................*P54282A0524*Turn over5(b) Plot these data on a scatter diagram on the grid below.(3)The managing director of AMG says ‘The scatter diagram shows positive correlation’.(c) Explain, in the context of the question, what this means.(1)............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................*P54282A0624*6When the data in the table are entered into a computer spreadsheet the following summary statistics are obtained.∑ x= 90 ∑ y= 52.68 ∑ xy= 506 ∑ x2 = 1140(d) Calculate the equation of the least squares regression line for yield of tomatoeson weight of fertiliser.(6).................................................................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................................................................... 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....................................................................................................................................................................................................................................................................................(e) Explain what the intercept and the gradient of the least squares regression linetell AMG.(3)Intercept .................................................................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................................................................... 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Gradient .................................................................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................................................................... ....................................................................................................................................................................................................................................................................................*P54282A0724*Turn over7(f) Estimate, using your equation in part (d), the weight of fertiliser needed for atomato plant to produce a yield of 5.20 kg.(3)........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................The correlation coefficient between weight of fertiliser and yield is 0.94(g) Discuss the reliability of your estimate in part (f).(2)................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(Total for Question 1 = 20 marks)*P54282A0824*82 The table shows the bonuses paid (x , $000) to a sample of 100 employees of LCV plc,an insurance company, in 2016Bonus paid (x , $000)Number of employees Total bonus payments x 4 7 14 4 < x 8 12 72 8 < x 9 20 170 9 < x 10 26 247 10 < x 16 29 37716 < x 246120(a) Calculate an estimate for the mean bonus.(3)....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(b) Calculate an estimate for the standard deviation.(4)........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................*P54282A0924*Turn over9(c) Give a reason why the standard deviation might be a better measure of spread touse in this case rather than the quartile deviation.(1)................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(d) Using your answers from parts (a) and (b), calculate the coefficient of variation forthese data.(2)....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(e) Explain what your answer to part (d) measures.(1)................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................*P54282A01024*10 The table of bonuses paid from page 8 is shown again here.Bonus paid (x, $000)Number of employees Total bonus paymentsx 4 7 144 < x 8 12 728 < x 9 20 1709 < x 10 26 24710 < x 16 29 37716 < x 24 6 120(f) Use these data to construct a Lorenz curve.(7)(g) Describe what the diagram shows about the distribution of bonuses paid in 2016(2) .................................................................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................................................................... ....................................................................................................................................................................................................................................................................................(Total for Question 2 = 20 marks)BLANK PAGEassurance manager has to test the batteries regularly to ensure that they satisfyquality standards.In a day, the factory produces 5000 batteries and each battery has a unique barcode.The quality assurance manager intends to select a sample of 120 of these batteries.(a) Give two reasons why the quality assurance manager would take a sample ratherthan a census of the batteries produced in a day.(2)1 ............................................................................................................................................................................................................................................................................... ....................................................................................................................................................................................................................................................................................2 ............................................................................................................................................................................................................................................................................... ....................................................................................................................................................................................................................................................................................(b) Suggest a suitable sampling frame for the quality assurance manager to use.(1) .................................................................................................................................................................................................................................................................................... ....................................................................................................................................................................................................................................................................................The quality assurance manager chooses to use simple random sampling to select the120 batteries.(c) Describe how the quality assurance manager would do this.(3) .................................................................................................................................................................................................................................................................................... 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.................................................................................................................................................................................................................................................................................... ........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(e) Estimate the modal time from the histogram.(3) .................................................................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................................................................... ....................................................................................................................................................................................................................................................................................(f) Estimate the percentage of these batteries that last less than 430 minutes.(3) 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....................................................................................................................................................................................................................................................................................One of these batteries is selected at random.(g) Calculate the probability that this battery lasted longer than 525 minutes.(2) .................................................................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................................................................... ....................................................................................................................................................................................................................................................................................(Total for Question 3 = 20 marks)。

《Business Statistic》中国人民大学出版社英文版第五版chapter1~8复习参考Part1名词解释1、Statistics is a method of extracting useful information from a set of numerical data in orderto make a more effective and informed decision.2、Descriptive Statistics：These are statistical methods of organizing, summarizing andpresenting numerical data in convenient forms such as graphs, charts and tables.3、Inferential statistics is defined as statistical methods used for drawing conclusions about apopulation based on samples.4、Primary data is obtained first hand.5、Secondary data already exists or has been previously collected such as company accounts, orsales figures.6、Mean: The arithmetic average and the most common measure ofaaaaaaa central tendency.①All values are included in computing the mean.②A set of data has a unique mean ③Themean is affected by unusually large or small data points (outliers / extreme values).7、Mode: The most frequent data, or data corresponding to the highest frequency. ①Mode isnot affected by extreme values. ②There may not be a mode. ③There may be several modes. ④Used for either numerical or categorical data.8、Median is the value that splits a ranked set of data into two equal parts. ①Median is notaffected by extremely large or small values and is therefore a valuable measure of central tendency when such values occur.9、Standard Deviation: ①A measure of the variation of data from the mean. ②The mostcommonly used measure of variation. ③Represented by the symbol ‘s’. ④Shows how the data is distributed around the mean.10、Probability is the chance of an occurrence of an event. ①Probability of an eventalways lies between 0 and 1. ②The sum of the probabilities of every possible outcome or event is 1. ③The probability of the complement A’ is given by 1-P(A).11、Properties of Normal distribution：①Continuous random variable. ②‘Bell-shaped’ &symmetrical. ③Mean, median, mode are equal ④Area under the curve is 1.12、The Central Limited Theorem：①If the population followed normal distribution, thesampling distribution of mean is followed normal distribution. ②If the population do not followed normal distribution, but the sample size is larger than 30, the sampling distribution of mean is followed normal distribution.Part2选择题Topic 1 - Introduction to Business Statistics & Data CollectionQ1. The universe or totality of items or things under consideration is called:a. a sample.b. a population.c. a parameter.d.none of the above.Q2. Those methods involving the collection, presentation, and characterization of a set of data in order to properly describe the various features of that set of data are called:a.inferential statistics.b.total quality management.c.sampling.d.descriptive statistics.Q3. The portion of the universe that has been selected for analysis is called:a. a sample.b. a frame.c. a parameter.d. a statistic.Q4. A summary measure that is computed to describe a numerical characteristic from only a sample of the population is called:a. a parameter.b. a census.c. a statistic.d.the scientific method.Q5. A summary measure that is computed to describe a characteristic of an entire population is called:a. a parameter.b. a census.c. a statistic.d.total quality management.Q6. The process of using sample statistics to draw conclusions about population parameters is called:a.inferential statistics.b.experimentation.c.primary sources.d.descriptive statistics.Q7. Which of the four methods of data collection is involved when a person retrieves data from an online databasea.published sources.b.experimentation.c.surveying.d.observation.Q8. Which of the four methods of data collection is involved when people are asked to complete a questionnairea.published sources.b.experimentation.c.surveying.d.observation.Q9. Which of the four methods of data collection is involved when a person records the use of the Los Angeles freeway systema.published sources.b.experimentation.c.surveying.d.observation.Q10. A focus group is an example of which of the four methods of data collectiona.published sources.b.experimentation.c.surveying.d.observation.Q11. Which of the following is true about response ratesa.The longer the questionnaire, the lower the rate.b.Mail surveys usually produce lower response rates than personal interviews or telephonesurveys.c.Question wording can affect a response rate.d. d. All of the above.Q12. Which of the following is a reason that a manager needs to know about statisticsa.To know how to properly present and describe information.b.To know how to draw conclusions about the population based on sample information.c.To know how to improve processes.d.All of the above.Scenario 1-1Questions 13-15 refer to this scenario:An insurance company evaluates many variables about a person before deciding on an appropriate rate for automobile insurance. Some of these variables can be classified as categorical, discrete and numerical, or continuous and numerical.Q13. Referring to Scenario 1-1 (above), the number of claims a person has made in the last three years is what type of variablea.Categorical.b.Discrete and numerical.c.Continuous and numerical.d.None of the above.Q14. Referring to Scenario 1-1 (above), a person's age is what type of variablea.Categorical.b.Discrete and numerical.c.Continuous and numerical.d.None of the above.Q15. Referring to Scenario 1-1 (above), a person's gender is what type of variablea.Categorical.b.Discrete and numerical.c.Continuous and numerical.d.None of the above.Q16. Which of the following can be reduced by proper interviewer traininga.Sampling error.b.Measurement error.c.Coverage error.d.Nonresponse error.Scenario 1-2Questions 17-19 refer to this scenario:Mediterranean fruit flies were discovered in California a few years ago and badly damaged the oranges grown in that state. Suppose the manager of a large farm wanted to study the impact of the fruit flies on the orange crops on a daily basis over a 6-week period. On each day a random sample of orange trees was selected from within a random sample of acres. The daily average number of damaged oranges per tree and the proportion of trees having damaged oranges were calculated.Q17. Referring to Scenario 1-2 (above), the two main measures calculated each day ., average number of damaged oranges per tree and proportion of trees having damaged oranges) are called _______.a.statistics.b.parameters.c.samples.d.populations.Q18. Referring to Scenario 1-2 (above), the two main measures calculated each day ., average number of damaged oranges per tree and proportion of trees having damaged oranges) may be used on a daily basis to estimate the respective true population _______.a.estimates.b.parameters.c.statistics.d.frame.Q19. Referring to Scenario 1-2 (above), in this study, drawing conclusions on any one day about the true population characteristics based on information obtained from the sample is called _______.a.evaluation.b.descriptive statistics.c.inferential statistics.d.survey.Scenario 1-3Questions 20 and 21 refer to this scenario:The Quality Assurance Department of a large urban hospital is attempting to monitor and evaluate patient satisfaction with hospital services. Prior to discharge, a random sample of patients is asked to fill out a questionnaire to rate such services as medical care, nursing, therapy, laboratory, food, and cleaning. The Quality Assurance Department prepares weekly reports that are presented at the Board of Directors meetings and extraordinary/atypical ratings are easy to flag.Q20. Referring to Scenario 1-3 (above), true population characteristics estimated from thesample results each week are called _____________.a.inferences.b.parameters.c.estimates.d.data.Q21. Referring to Scenario 1-3 (above), a listing of all hospitalised patients in this institution over a particular week would constitute the ________.a.sample.b.population.c.statistics.d.parameters.Scenario 1-4Questions 22-24 refer to this scenario:The following are the questions given to Sheila Drucker-Ferris in her college alumni association survey. Each variable can be classified as categorical or numerical, discrete or continuous.Q22. Referring to Scenario 1-4 (above), the data for the number of years since graduation is categorised as: __________________.a.numerical discrete.b.categorical.c.numerical continuous.d.none of the above.Q23. Referring to Scenario 1-4 (above), the data for the number of science majors is categorised as: ____________.a.categorical.b.numerical continuous.c.numerical discrete.d.none of the above.Q24. Referring to Scenario 1-4 (above), the data for tabulating the level of job satisfaction (High, Moderate, Low) is categorised as: _________.a.numerical continuous.b.categorical.c.numerical discrete.d.none of the above.Topic 2: Organising and Presenting dataQ1 The width of each bar in a histogram corresponds to the:a.boundaries of the classes.b.number of observations in the classes.c.midpoint of the classes.d.percentage of observations in the classes.Q2 When constructing charts, which of the following chart types is plotted at the class midpointsa.Frequency histograms.b.Percentage polygons.c.Cumulative relative frequency ogives.d.Relative frequency histograms.Q3 When polygons or histograms are constructed, which axis must show the true zero or "origin"a.The horizontal axis.b.The vertical axis.c.Both the horizontal and vertical axes.d.Neither the horizontal nor the vertical axis.Q4 To determine the appropriate width of each class interval in a grouped frequency distribution, we:a.divide the range of the data by the number of desired class intervals.b.divide the number of desired class intervals by the range of the datac.take the square root of the number of observations.d.take the square of the number of observations.Q5 When grouping data into classes it is recommended that we have:a.less than 5 classes.b.between 5 and 15 classes.c.more than 15 classes.d.between 10 and 30 classes.Q6 Which of the following charts would give you information regarding the number of observations "up to and including" a given groupa.Frequency histograms.b.Polygons.c.Percentage polygons.d.Cumulative relative frequency ogives.Q7 Another name for an "ogive" is a:a.frequency histogram.b.polygon.c.percentage polygon.d.cumulative percentage polygon.Q8 In analyzing categorical data, the following graphical device is NOT appropriate:a.bar chart.b.Pareto diagram.c.stem and leaf display.d.pie chart.Table 2The opinions of a sample of 200 people broken down by gender about the latest congressionalQ9 Table 2 (above) contains the opinions of a sample of 200 people broken down by gender about the latest congressional plan to eliminate anti-trust exemptions for professional baseball. Referring to Table 2, the number of people who are neutral to the plan is _______.a.36b.54c.90d.200Q10 Referring to Table 2, the number of males who are against the plan is _______.a.12b.48c.60d.96Q11 Referring to Table 2, the percentage of males among those who are for the plan is ______.a.%b.24%c.25%d.76%Q12 Referring to Table 2, the percentage who are against the plan among the females is _______.a.%b.20%c.30%d.52%Topic 3: Numerical Descriptive StatisticsQ1 Which measure of central tendency can be used for both numerical and categorical variablesa.Mean.b.Median.c.Mode.d.Quartiles.Q2 Which of the following statistics is not a measure of central tendencya.Mean.b.Median.c.Mode.d.Q3.Q3 Which of the following statements about the median is NOT truea.It is more affected by extreme values than the mean.b.It is a measure of central tendency.c.It is equal to Q2.d.It is equal to the mode in bell-shaped distributions.Q4 The value in a data set that appears most frequently is called:a.the median.b.the mode.c.the mean.d.the variance.Q5 In a perfectly symmetrical distribution:a.the mean equals the median.b.the median equals the mode.c.the mean equals the mode.d.All of the above.Q6 When extreme values are present in a set of data, which of the following descriptive summary measures are most appropriatea.CV and range.b.Mean and standard deviation.c.Median and interquartile range.d.Mode and variance.Q7 The smaller the spread of scores around the mean:a.the smaller the interquartile range.b.the smaller the standard deviation.c.the smaller the coefficient of variation.d.All the above.Q8 In a right-skewed distribution:a.the median equals the mean.b.the mean is less than the median.c.the mean is greater than the median.d.the mean is less than the mode.a.b.c.d.Q10 Referring to Table 3 (above), the median carbohydrate amount in the cereal is ________ grams.a.19b.20c.21d.Q11 Referring to Table 3 (above), the 1st quartile of the carbohydrate amounts is ________ grams.a.15b.20c.21d.25Q12 Referring to Table 3 (above), the range in the carbohydrate amounts is ________ grams.a.16b.18c.20d.21Topic 4: Basics probability and discrete probability distributionsInformation A, needed to answer Questions 1 to 2The Health and Safety committee in a large retail firm is examining the relationship between the number of days of sick leave an employee takes and whether an employee works on the day shift (D) or night shift (N). The committee looks at a sample of 50 employees and notes which shift they work on and whether the number of days of sick leave they take in a year is less than 6 daysQ1 Use Information A to answer this question. Which of the following statements about the values in the table of probabilities is not correcta.The probability of an employee taking 6 or more days of sick leave P(M) isb.The probability that an employee is on the Night Shift (N) and takes less than 6 days ofleave (L), is called a conditional probability P(N | L) =c.If you know that an employee is on day shift (D) then the probability that they will takeless than 6 days of leave (L) is the conditional probability P(L | D) =d.The probability that an employee works Day Shift (D) or takes 6 or more days of leave (M)is found using the addition rule to be P(D or M) =e.They are all correctQ2 The analyst wishes to use the Probabilities table from Information A to determine whether the work shift variable and the number of days of sick leave variable are or are not independent variables. Which of the following statements about the work shift and the number of days of sick leave variables is correcta.These variables are independent because the marginal probabilities such as P(L) are thesame as the conditional probabilities P(L | D)b.These variables are not independent because the marginal probability P(L) is differentfrom the conditional probability P(N | L)c.These variables are not independent because the joint probabilities such as P(L and N)are equal to the product of the probabilities P(L).P(N).d.These variables are dependent because the marginal probabilities such as P(L) are equalto the conditional probability P(L | N)e.None of the aboveInformation B, needed to answer Question 3Suppose the manager of a home ware retailer decides in a 5-minute period no more than 4 customers can arrive at a counter. Using past records he obtains the following probabilitythe following is the correct pair of values for the mean, the variance or standard deviation of the number of arrivals at the counter.a.Mean mu = 2 and variance sigma-squared =b.Mean mu = and variance sigma-squared =c.Mean mu = 2 and standard deviation sigma =d.Mean mu = and variance sigma-squared =e.None of the aboveInformation C, needed to answer Questions 4-6The section manager in an insurance company is interested in evaluating how well staff at the inquiry counter handle customer complaints. She interviews a sample of n = 6 customers who have made complaints and asks each of them whether staff had handled their complaints well. Each interview is called a trial. If a customer says their complaint was handled well this is called a success. She thinks that as long as these people are interviewed independently of each other then the number of people who say their complaint was handled well is a random variable with a Binomial probability distribution. The section manager thinks that the probability that a customers complaint will be handled well is p = .Q4 Use Information C to answer this question. A total of n = 6 people are interviewed independently of each other. Which of the following statements about the probability that 5 out of the 6 complaints will be handled well is correcta.less thanb.between andc.more thand.between ande.None of the aboveQ5 Using Information C, which of the following statements about the probability that 4 or less of the 6 complaints will be handled well is correcta.less thanb.more thanc.between andd.between ande.None of the aboveQ6 Suppose the section manager from Information C is interested in the measures of central tendency and variation for the number of complaints which are handled well. Which of the following sets of values, where values are rounded to 3 decimal places, is the correct set of valuesa.Mean mu = and variance sigma-squared =b.Mean mu = and variance sigma-squared =c.Mean mu = and variance sigma-squared =d.Mean mu = and standard deviation sigma =e.None of the aboveInformation D, needed to answer Questions 7-9The manager of a large retailer thinks that one reason why staff at the complaints counter fail to handle customer complaints well is that not enough staff are allocated to this counter. Past experience has shown that the number of customers who arrive at this counter has a Poisson distribution where the average number who arrive each hour is 36. He decides to look at how many customers are likely to arrive at the complaints counter during a 5-minute period.Q7 Use Information D to answer this question. Which of the following statements concerning the probability that exactly 2 customers will arrive at the counter in a 5-minute period is correcta.less thanb.between andc.between andd.more thane.None of the aboveQ8 Use Information D to answer this question. Which of the following statements concerning the probability that 3 or more customers will arrive at a counter in a 5-minute period is correcta.between andb.less thanc.more thand.between ande.None of the aboveQ9 The section manager from Information D is interested in the mean and variance of the number of customers who arrive during a 1 hour period. Which of the following is the correct set of values for these two measuresa.Mean mu = 3 and variance sigma-squared = 3b.Mean mu = 36 and standard deviation sigma =c.Mean mu = 30 and variance sigma-squared = 30d.Mean mu = 36 and standard deviation sigma = 6e.None of the aboveTopic 5: Normal probability distribution & sampling distributionQ1 Which of the following is not a property of the normal distributiona.It is bell-shaped.b.It is slightly skewed left.c.Its measures of central tendency are all identical.d.Its range is from negative infinity to positive infinity.Q2 The area under the standardized normal curve from 0 to would be:a.the same as the area from 0 to .b.equal to .c.found by using Table in your textbook.d.all of the above.Q3 Which of the following about the normal distribution is not truea.Theoretically, the mean, median, and mode are the same.b.About two-thirds of the observations fall within ± 1 standard deviation from the mean.c.It is a discrete probability distribution.d.Its parameters are the mean and standard deviation.Q4 In its standardized form, the normal distribution:a.has a mean of 0 and a standard deviation of 1.b.has a mean of 1 and a variance of 0.c.has a total area equal to .d.cannot be used to approximate discrete binomial probability distributions.Q5 In the standardized normal distribution, the probability that Z > 0 is _______.a.b.c.d.cannot be found without more informationQ6 The probability of obtaining a value greater than 110 in a normal distribution in which the mean is 100 and the standard deviation is 10 is ______________ the probability of obtaining a value greater than 650 in a normal distribution with a mean of 500 and a standard deviation of 100.a.less thanb.equal to.c.greater thand.It is unknown without more information.Q7 The probability of getting a Z score greater than is ________.a.close tob.c. a negative numberd.almost zeroQ8 For some positive value of Z, the probability that a standardized normal variable is between 0 and Z is . The value of Z isa.b.c.d.Q9 For some value of Z, the probability that a standardized normal variable is below Z is . The value of Z isa.b.c.d.Q10 Given that X is a normally distributed random variable with a mean of 50 and a standard deviation of 2, the probability that X is between 47 and 54 isa.b.c.d.Q11 For some positive value of X, the probability that a standardized normal variable is between 0 and + is . The value of X isa.b.c.d.Q12 The owner of a fish market determined that the average weight for a catfish is pounds with a standard deviation of pounds. A citation catfish should be one of the top 2 percent in weight. Assuming the weights of catfish are normally distributed, at what weight (in pounds) should the citation designation be establisheda.poundsb.poundsc.poundsd.poundsQ13 Which of the following is NOT a property of the arithmetic meana.It is unbiased.b.It is always equal to the population mean.c.Its average is equal to the population mean.d.Its variance becomes smaller when the sample size gets bigger.Q14 The sampling distribution of the mean is a distribution of:a.individual population values.b.individual sample values.c.statistics.d.parameters.Q15 The standard deviation of the sampling distribution of the mean is called the:a.standard error of the sample.b.standard error of the estimate.c.standard error of the mean.d.All of the aboveQ16 According to the central limit theorem, the sampling distribution of the mean can be approximated by the normal distribution:a.as the number of samples gets "large enough."b.as the sample size (number of observations) gets "large enough."c.as the size of the population standard deviation increases.d.as the size of the sample standard deviation decreases.Q17 For a sample size of n=10, the sampling distribution of the mean will be normally distributed:a.regardless of the population's distribution.b.if the shape of the population is symmetrical.c.if the variance of the mean is known.d.if the population is normally distributedTopic 6: EstimationQ1 The interval estimate using the t critical value is ________ than the interval estimate using the z critical value.a.Narrowerb.The same asc.Widerd.More powerfulQ2 To estimate the mean of a normal population with unknown standard deviation using a small sample, we use the ______ distribution.a.'t'b.'Z'c.samplingd.alphaQ3 If the population does not follow a normal distribution, then to use the t distribution to give a confidence interval estimate for the population mean, the sample size should be:a.at least 5b.at least 30c.at least 100d.less than 30Q4 The 'z' value or 't' value used in the confidence interval formula is called the:a.sigma valueb.critical valuec.alpha valued.none of the aboveQ5 The 'z' value that is used to construct a 90 percent confident interval is:a.b.c.d.Q6 The 'z' value that is used to construct a 95 percent confidence interval is:a.b.c.d.Q7 The sample size needed to construct a 90 percent confidence interval estimate for the population mean with sampling error ± when sigma is known to be 10 units is:a.9b.32c.75d.107Q8 The t critical value approaches the z critical value when:a.the sample size decreasesb.the sample size approaches infinityc.the confidence level increasesd.the sample is smallQ9 The t-critical value used when constructing a 99 percent confidence interval estimate with a sample of size 18 is:a.b.c.d.Q10 The t-value that would be used to construct a 90 percent confidence interval for the mean with a sample of size n 36 would be:a.b.c.d.Q11 The value of alpha (two tailed) for a 96 percent confidence interval would be: a.b.c.d.Q12 When using the t distribution for confidence interval estimates for the mean, the degrees of freedom value is:a.nb.n-1c.n-2d.n %2B 1Q13 You would interpret a 90 percent confidence interval for the population mean as:a.you can be 90 percent confident that you have selected a sample whose interval doesinclude the population meanb.if all possible samples are selected and CI's are calculated, 90 percent of those intervalswould include the true population meanc.90 percent of the population is in that intervald.both A and B are trueQ14 From a sample of 100 items, 30 were defective. A 95 percent confidence interval for the proportion of defectives in the population is:a.(.2, .4)b.(.21, .39)c.(.225, .375)d.(.236, .364)Q15 A confidence interval was used to estimate the proportion of statistics students that are male. A random sample of 70 statistics students generated the following 90 percent confidence interval: , . Using the information above, what size sample would be necessary if we wanted to estimate the true proportion to within ± using 95 percent confidencea.240b.450c.550d.150整理人：阿桤。

HOMEWORK OF THE BUSINESS STATISTICSMAJOR: MANAGEMENT SCIENCENAME: MENG ZEHUASTUDENT ID: 2009012361SOLUTION:(a). From the question we can know that the sample mean is X =9.7 days and the samplestandard deviation is S=4.0 days. Using the row for 24 degrees of freedom, for 95% confidence, we can find /2t α= from the table. Since n=25, using Equation,11.3511204888.8 1.651129.7)25(4.0/ 2.0639 9.7nS t X /2≤≤±=±=±μαWe are 95% confident that the mean number of absences for clerical workers during the year is between days .Although the true mean may or may not be in this interval, 95% of intervals formed in this manner will contain the true mean.(b).Since X =12 >5 , n-X=13 >5 , using Equation, P=n X =2512=0.48, and with a 95% level of confidence /2Z α, 0.1960.48 /250.48(0.52)1.9648.0p)/np(1Z p /2±=±=-±α0.676 0.284≤≤πWe are 95% confident that the population proportion of clerical workers absent more than 10 days during the year is between 0.284 and 0.676. Although the interval from to may or may not contain the true proportion, 95% of intervals formed from samples of size 25 in this manner will contain the true proportion.(c).Using Equation and e=1.5, σ=4.5,and /2Z α=1.96 for 95% confidence,2222/σe Z n α==222)5.1((4.5))96.1(=35 Therefore, we should select a sample size of 35 clerical workers because the general rule for determining sample size is to always round up to the next integer value in order to slightlyoversatisfy the criteria desired.(d).Because no information is available from past data, assume that π=0.50.75, π=0.50,and /2Z α=1.645 for 90% confidence,121(0.075)0.50)(0.50)(1(1.645)e )(1Z n 2222/2=-=-=ππα Therefore you need a sample of 121 clerical workers to estimate the population proportion to within ±0.075 with 90% confidence.(e).If a single sample were to be selected for both purposes, the larger of the two sample sizes (n=121) should be used.SOLUTION:(a).From the question we can know that the sample mean is X =$ and the sample standard deviation is S=$. Using the row for 59 degrees of freedom, for 95% confidence, we can find /2t α010 from the table. Since n=60, using Equation,40.415665.36 1.87554.83)60(7.26/ 2.0010 38.54nS t X /2≤≤±=±=±μαWe are 95% confident that the population mean amount spent per customer in the restaurant is between $ and $.Although the true mean may or may not be in this interval, 95% of intervals formed in this manner will contain the true mean.(b). Since X =18 >5 , n-X=42 >5 , using Equation, P=n X =6018=, and with a 90% level of confidence /2Z α= 1.645, 0.09730.3 00.3(0.7)/61.6453.0p)/np(1Z p /2±=±=-±α0.3973 0.2027≤≤πWe are 90% confident that the population proportion of customers who purchase dessert isbetween 0.2027 and 0.3973. Although the interval from 027 to 0.3973 may or may not contain the true proportion, 90% of intervals formed from samples of size 60 in this manner will contain the true proportion.(c).Using Equation and e=, σ=8, and /2Z α=1.96 for 95% confidence,2222/σe Z n α==222)50.1(8*)96.1(=110 Therefore, we should select a sample size of 110 customers because the general rule for determining sample size is to always round up to the next integer value in order to slightly oversatisfy the criteria desired.(d).Because no information is available from past data, assume that π=0.50.4, π=0.50,and /2Z α=1.645 for 90% confidence,423(0.04)0.50)(0.50)(1(1.645)e )(1Z n 2222/2=-=-=ππα Therefore you need a sample of 423 customers to estimate the population proportion to within ±4 with 90% confidence.(e).If a single sample were to be selected for both purposes, the larger of the two sample sizes (n=423) should be used.SOLUTION:(a)&(b). Using the calculator we can know that the sample mean is X =8.421 inches and the sample standard deviation is S=0.046 inches. Using the row for 48 degrees of freedom, for 95% confidence, we can find /2t α= from the table. Since n=49, using Equation,8.43424078.80.0132421.8)49(0.046/ 2.0106 8.421nS t X /2≤≤±=±=±μαWe are 95% confident that the mean width of the troughs is between and 8.4342 inches.Although the true mean may or may not be in this interval, 95% of intervals formed in this manner will contain the true mean.(c).The assumption is valid as the width of the troughs is approximately normally distributed.HOMEWORK OF THE BUSINESS STATISTICSMAJOR: MANAGEMENT SCIENCENAME: MENG ZEHUASTUDENT ID: 2009012361SOLUTION:(a). From the question we can know that the sample mean is X =9.7 days and the samplestandard deviation is S=4.0 days. Using the row for 24 degrees of freedom, for 95% confidence, we can find /2t α= from the table. Since n=25, using Equation,11.3511204888.8 1.651129.7)25(4.0/ 2.0639 9.7nS t X /2≤≤±=±=±μαWe are 95% confident that the mean number of absences for clerical workers during the year is between days .Although the true mean may or may not be in this interval, 95% of intervals formed in this manner will contain the true mean.(b).Since X =12 >5 , n-X=13 >5 , using Equation, P=n X =2512=0.48, and with a 95% level of confidence /2Z α, 0.1960.48 /250.48(0.52)1.9648.0p)/np(1Z p /2±=±=-±α0.676 0.284≤≤πWe are 95% confident that the population proportion of clerical workers absent more than 10 days during the year is between 0.284 and 0.676. Although the interval from to may or may not contain the true proportion, 95% of intervals formed from samples of size 25 in this manner will contain the true proportion.(c).Using Equation and e=1.5, σ=4.5,and /2Z α=1.96 for 95% confidence,2222/σe Z n α==222)5.1((4.5))96.1(=35 Therefore, we should select a sample size of 35 clerical workers because the general rule for determining sample size is to always round up to the next integer value in order to slightlyoversatisfy the criteria desired.(d).Because no information is available from past data, assume that π=0.50.75, π=0.50,and /2Z α=1.645 for 90% confidence,121(0.075)0.50)(0.50)(1(1.645)e )(1Z n 2222/2=-=-=ππα Therefore you need a sample of 121 clerical workers to estimate the population proportion to within ±0.075 with 90% confidence.(e).If a single sample were to be selected for both purposes, the larger of the two sample sizes (n=121) should be used.SOLUTION:(a).From the question we can know that the sample mean is X =$ and the sample standard deviation is S=$. Using the row for 59 degrees of freedom, for 95% confidence, we can find /2t α010 from the table. Since n=60, using Equation,40.415665.36 1.87554.83)60(7.26/ 2.0010 38.54nS t X /2≤≤±=±=±μαWe are 95% confident that the population mean amount spent per customer in the restaurant is between $ and $.Although the true mean may or may not be in this interval, 95% of intervals formed in this manner will contain the true mean.(b). Since X =18 >5 , n-X=42 >5 , using Equation, P=n X =6018=, and with a 90% level of confidence /2Z α= 1.645, 0.09730.3 00.3(0.7)/61.6453.0p)/np(1Z p /2±=±=-±α0.3973 0.2027≤≤πWe are 90% confident that the population proportion of customers who purchase dessert isbetween 0.2027 and 0.3973. Although the interval from 027 to 0.3973 may or may not contain the true proportion, 90% of intervals formed from samples of size 60 in this manner will contain the true proportion.(c).Using Equation and e=, σ=8, and /2Z α=1.96 for 95% confidence,2222/σe Z n α==222)50.1(8*)96.1(=110 Therefore, we should select a sample size of 110 customers because the general rule for determining sample size is to always round up to the next integer value in order to slightly oversatisfy the criteria desired.(d).Because no information is available from past data, assume that π=0.50.4, π=0.50,and /2Z α=1.645 for 90% confidence,423(0.04)0.50)(0.50)(1(1.645)e )(1Z n 2222/2=-=-=ππα Therefore you need a sample of 423 customers to estimate the population proportion to within ±4 with 90% confidence.(e).If a single sample were to be selected for both purposes, the larger of the two sample sizes (n=423) should be used.SOLUTION:(a)&(b). Using the calculator we can know that the sample mean is X =8.421 inches and the sample standard deviation is S=0.046 inches. Using the row for 48 degrees of freedom, for 95% confidence, we can find /2t α= from the table. Since n=49, using Equation,8.43424078.80.0132421.8)49(0.046/ 2.0106 8.421nS t X /2≤≤±=±=±μαWe are 95% confident that the mean width of the troughs is between and 8.4342 inches.Although the true mean may or may not be in this interval, 95% of intervals formed in this manner will contain the true mean.(c).The assumption is valid as the width of the troughs is approximately normally distributed.。

《Business Statistic》中国人民大学出版社英文版第五版chapter1~8复习参考Part1名词解释1、Statistics is a method of extracting useful information from a set of numerical data in order tomake a more effective and informed decision.2、Descriptive Statistics：These are statistical methods of organizing, summarizing andpresenting numerical data in convenient forms such as graphs, charts and tables.3、Inferential statistics is defined as statistical methods used for drawing conclusions about apopulation based on samples.4、Primary data is obtained first hand.5、Secondary data already exists or has been previously collected such as company accounts, orsales figures.6、Mean: The arithmetic average and the most common measure ofaaaaaaa central tendency. ①All values are included in computing the mean.②A set of data has a unique mean ③The mean is affected by unusually large or small data points (outliers / extreme values).7、Mode: The most frequent data, or data corresponding to the highest frequency. ①Mode is notaffected by extreme values. ②There may not be a mode. ③There may be several modes. ④Used for either numerical or categorical data.8、Median is the value that splits a ranked set of data into two equal parts. ①Median is notaffected by extremely large or small values and is therefore a valuable measure of central tendency when such values occur.9、Standard Deviation: ①A measure of the variation of data from the mean. ②The mostcommonly used measure of variation. ③Represented by the symbol ‘s’. ④Shows how the data is distributed around the mean.10、Probability is the chance of an occurrence of an event. ①Probability of an eventalways lies between 0 and 1. ②The sum of the probabilities of every possible outcome or event is 1. ③The probability of the complement A’ is given by 1-P(A).11、Properties of Normal distribution：①Continuous random variable. ②‘Bell-shaped’ &symmetrical. ③Mean, median, mode are equal ④Area under the curve is 1.12、The Central Limited Theorem：①If the population followed normal distribution, thesampling distribution of mean is followed normal distribution. ②If the population do not followed normal distribution, but the sample size is larger than 30, the sampling distribution of mean is followed normal distribution.Part2选择题Topic 1 - Introduction to Business Statistics & Data CollectionQ1. The universe or totality of items or things under consideration is called:a. a sample.b. a population.c. a parameter.d.none of the above.Q2. Those methods involving the collection, presentation, and characterization of a set of data in order to properly describe the various features of that set of data are called:a.inferential statistics.b.total quality management.c.sampling.d.descriptive statistics.Q3. The portion of the universe that has been selected for analysis is called:a. a sample.b. a frame.c. a parameter.d. a statistic.Q4. A summary measure that is computed to describe a numerical characteristic from only a sample of the population is called:a. a parameter.b. a census.c. a statistic.d.the scientific method.Q5. A summary measure that is computed to describe a characteristic of an entire population is called:a. a parameter.b. a census.c. a statistic.d.total quality management.Q6. The process of using sample statistics to draw conclusions about population parameters is called:a.inferential statistics.b.experimentation.c.primary sources.d.descriptive statistics.Q7. Which of the four methods of data collection is involved when a person retrieves data from an online database?a.published sources.b.experimentation.c.surveying.d.observation.Q8. Which of the four methods of data collection is involved when people are asked to complete a questionnaire?a.published sources.b.experimentation.c.surveying.d.observation.Q9. Which of the four methods of data collection is involved when a person records the use of the Los Angeles freeway system?a.published sources.b.experimentation.c.surveying.d.observation.Q10. A focus group is an example of which of the four methods of data collection?a.published sources.b.experimentation.c.surveying.d.observation.Q11. Which of the following is true about response rates?a.The longer the questionnaire, the lower the rate.b.Mail surveys usually produce lower response rates than personal interviews or telephonesurveys.c.Question wording can affect a response rate.d. d. All of the above.Q12. Which of the following is a reason that a manager needs to know about statistics?a.To know how to properly present and describe information.b.To know how to draw conclusions about the population based on sample information.c.To know how to improve processes.d.All of the above.Scenario 1-1Questions 13-15 refer to this scenario:An insurance company evaluates many variables about a person before deciding on an appropriate rate for automobile insurance. Some of these variables can be classified as categorical, discrete and numerical, or continuous and numerical.Q13. Referring to Scenario 1-1 (above), the number of claims a person has made in the last three years is what type of variable?a.Categorical.b.Discrete and numerical.c.Continuous and numerical.d.None of the above.Q14. Referring to Scenario 1-1 (above), a person's age is what type of variable?a.Categorical.b.Discrete and numerical.c.Continuous and numerical.d.None of the above.Q15. Referring to Scenario 1-1 (above), a person's gender is what type of variable?a.Categorical.b.Discrete and numerical.c.Continuous and numerical.d.None of the above.Q16. Which of the following can be reduced by proper interviewer training?a.Sampling error.b.Measurement error.c.Coverage error.d.Nonresponse error.Scenario 1-2Questions 17-19 refer to this scenario:Mediterranean fruit flies were discovered in California a few years ago and badly damaged the oranges grown in that state. Suppose the manager of a large farm wanted to study the impact of the fruit flies on the orange crops on a daily basis over a 6-week period. On each day a random sample of orange trees was selected from within a random sample of acres. The daily average number of damaged oranges per tree and the proportion of trees having damaged oranges were calculated.Q17. Referring to Scenario 1-2 (above), the two main measures calculated each day (i.e., average number of damaged oranges per tree and proportion of trees having damaged oranges) are called _______.a.statistics.b.parameters.c.samples.d.populations.Q18. Referring to Scenario 1-2 (above), the two main measures calculated each day (i.e., average number of damaged oranges per tree and proportion of trees having damaged oranges) may be used on a daily basis to estimate the respective true population _______.a.estimates.b.parameters.c.statistics.d.frame.Q19. Referring to Scenario 1-2 (above), in this study, drawing conclusions on any one day about the true population characteristics based on information obtained from the sample is called _______.a.evaluation.b.descriptive statistics.c.inferential statistics.d.survey.Scenario 1-3Questions 20 and 21 refer to this scenario:The Quality Assurance Department of a large urban hospital is attempting to monitor and evaluate patient satisfaction with hospital services. Prior to discharge, a random sample of patients is asked to fill out a questionnaire to rate such services as medical care, nursing, therapy, laboratory, food, and cleaning. The Quality Assurance Department prepares weekly reports that are presented at the Board of Directors meetings and extraordinary/atypical ratings are easy to flag.Q20. Referring to Scenario 1-3 (above), true population characteristics estimated from the sample results each week are called _____________.a.inferences.b.parameters.c.estimates.d.data.Q21. Referring to Scenario 1-3 (above), a listing of all hospitalised patients in this institution over a particular week would constitute the ________.a.sample.b.population.c.statistics.d.parameters.Scenario 1-4Questions 22-24 refer to this scenario:The following are the questions given to Sheila Drucker-Ferris in her college alumni association survey. Each variable can be classified as categorical or numerical, discrete or continuous.Q22. Referring to Scenario 1-4 (above), the data for the number of years since graduation is categorised as: __________________.a.numerical discrete.b.categorical.c.numerical continuous.d.none of the above.Q23. Referring to Scenario 1-4 (above), the data for the number of science majors is categorised as: ____________.a.categorical.b.numerical continuous.c.numerical discrete.d.none of the above.Q24. Referring to Scenario 1-4 (above), the data for tabulating the level of job satisfaction (High, Moderate, Low) is categorised as: _________.a.numerical continuous.b.categorical.c.numerical discrete.d.none of the above.Topic 2: Organising and Presenting dataQ1 The width of each bar in a histogram corresponds to the:a.boundaries of the classes.b.number of observations in the classes.c.midpoint of the classes.d.percentage of observations in the classes.Q2 When constructing charts, which of the following chart types is plotted at the class midpoints?a.Frequency histograms.b.Percentage polygons.c.Cumulative relative frequency ogives.d.Relative frequency histograms.Q3 When polygons or histograms are constructed, which axis must show the true zero or "origin"?a.The horizontal axis.b.The vertical axis.c.Both the horizontal and vertical axes.d.Neither the horizontal nor the vertical axis.Q4 To determine the appropriate width of each class interval in a grouped frequency distribution, we:a.divide the range of the data by the number of desired class intervals.b.divide the number of desired class intervals by the range of the datac.take the square root of the number of observations.d.take the square of the number of observations.Q5 When grouping data into classes it is recommended that we have:a.less than 5 classes.b.between 5 and 15 classes.c.more than 15 classes.d.between 10 and 30 classes.Q6 Which of the following charts would give you information regarding the number of observations "up to and including" a given group?a.Frequency histograms.b.Polygons.c.Percentage polygons.d.Cumulative relative frequency ogives.Q7 Another name for an "ogive" is a:a.frequency histogram.b.polygon.c.percentage polygon.d.cumulative percentage polygon.Q8 In analyzing categorical data, the following graphical device is NOT appropriate:a.bar chart.b.Pareto diagram.c.stem and leaf display.d.pie chart.Table 2The opinions of a sample of 200 people broken down by gender about the latest congressional For Neutral Against Totals Female 38 54 12 104Male 12 36 48 96Q9 Table 2 (above) contains the opinions of a sample of 200 people broken down by gender about the latest congressional plan to eliminate anti-trust exemptions for professional baseball. Referring to Table 2, the number of people who are neutral to the plan is _______.a.36b.54c.90d.200Q10 Referring to Table 2, the number of males who are against the plan is _______.a.12b.48c.60d.96Q11 Referring to Table 2, the percentage of males among those who are for the plan is ______.a.12.5%b.24%c.25%d.76%Q12 Referring to Table 2, the percentage who are against the plan among the females is _______.a.11.54%b.20%c.30%d.52%Topic 3: Numerical Descriptive StatisticsQ1 Which measure of central tendency can be used for both numerical and categorical variables?a.Mean.b.Median.c.Mode.d.Quartiles.Q2 Which of the following statistics is not a measure of central tendency?a.Mean.b.Median.c.Mode.d.Q3.Q3 Which of the following statements about the median is NOT true?a.It is more affected by extreme values than the mean.b.It is a measure of central tendency.c.It is equal to Q2.d.It is equal to the mode in bell-shaped distributions.Q4 The value in a data set that appears most frequently is called:a.the median.b.the mode.c.the mean.d.the variance.Q5 In a perfectly symmetrical distribution:a.the mean equals the median.b.the median equals the mode.c.the mean equals the mode.d.All of the above.Q6 When extreme values are present in a set of data, which of the following descriptive summary measures are most appropriate?a.CV and range.b.Mean and standard deviation.c.Median and interquartile range.d.Mode and variance.Q7 The smaller the spread of scores around the mean:a.the smaller the interquartile range.b.the smaller the standard deviation.c.the smaller the coefficient of variation.d.All the above.Q8 In a right-skewed distribution:a.the median equals the mean.b.the mean is less than the median.c.the mean is greater than the median.d.the mean is less than the mode.Q9 Referring to Table 3 (above), the mean carbohydrates in this sample is ________ grams.a.15.25b.19.73c.21.42d.21.70Q10 Referring to Table 3 (above), the median carbohydrate amount in the cereal is ________ grams.a.19b.20c.21d.21.5Q11 Referring to Table 3 (above), the 1st quartile of the carbohydrate amounts is ________ grams.a.15b.20c.21d.25Q12 Referring to Table 3 (above), the range in the carbohydrate amounts is ________ grams.a.16b.18c.20d.21Topic 4: Basics probability and discrete probability distributionsInformation A, needed to answer Questions 1 to 2The Health and Safety committee in a large retail firm is examining the relationship between the number of days of sick leave an employee takes and whether an employee works on the day shift (D) or night shift (N). The committee looks at a sample of 50 employees and notes which shift they work on and whether the number of days of sick leave they take in a year is less than 6 daysQ1 Use Information A to answer this question. Which of the following statements about the values in the table of probabilities is not correct?a.The probability of an employee taking 6 or more days of sick leave P(M) is 0.6b.The probability that an employee is on the Night Shift (N) and takes less than 6 days ofleave (L), is called a conditional probability P(N | L) = 0.6c.If you know that an employee is on day shift (D) then the probability that they will takeless than 6 days of leave (L) is the conditional probability P(L | D) = 0.4d.The probability that an employee works Day Shift (D) or takes 6 or more days of leave(M) is found using the addition rule to be P(D or M) = 0.76e.They are all correctQ2 The analyst wishes to use the Probabilities table from Information A to determine whether the work shift variable and the number of days of sick leave variable are or are not independent variables. Which of the following statements about the work shift and the number of days of sickleave variables is correct ?a.These variables are independent because the marginal probabilities such as P(L) are thesame as the conditional probabilities P(L | D)b.These variables are not independent because the marginal probability P(L) is differentfrom the conditional probability P(N | L)c.These variables are not independent because the joint probabilities such as P(L and N) areequal to the product of the probabilities P(L).P(N).d.These variables are dependent because the marginal probabilities such as P(L) are equalto the conditional probability P(L | N)e.None of the aboveInformation B, needed to answer Question 3Suppose the manager of a home ware retailer decides in a 5-minute period no more than 4 customers can arrive at a counter. Using past records he obtains the following probabilityTable 4-3Arrivals (X) 0 1 2 3 4P(X) .15 .20 .30 .20 .15Q3 Use Information B to answer this question. If values are rounded to 3 decimal places which of the following is the correct pair of values for the mean, the variance or standard deviation of the number of arrivals at the counter.a.Mean mu = 2 and variance sigma-squared = 1.265b.Mean mu = 2.5 and variance sigma-squared = 1.6c.Mean mu = 2 and standard deviation sigma = 1.6d.Mean mu = 2.4 and variance sigma-squared = 1.6e.None of the aboveInformation C, needed to answer Questions 4-6The section manager in an insurance company is interested in evaluating how well staff at the inquiry counter handle customer complaints. She interviews a sample of n = 6 customers who have made complaints and asks each of them whether staff had handled their complaints well. Each interview is called a trial. If a customer says their complaint was handled well this is called a success. She thinks that as long as these people are interviewed independently of each other then the number of people who say their complaint was handled well is a random variable with a Binomial probability distribution. The section manager thinks that the probability that a customers complaint will be handled well is p = 0.75.Q4 Use Information C to answer this question. A total of n = 6 people are interviewed independently of each other. Which of the following statements about the probability that 5 out of the 6 complaints will be handled well is correcta.less than 0.06b.between 0.23 and 0.24c.more than 0.35d.between 0.30 and 0.32e.None of the aboveQ5 Using Information C, which of the following statements about the probability that 4 or less of the 6 complaints will be handled well is correcta.less than 0.36b.more than 0.52c.between 0.45 and 0.475d.between 0.15 and 0.175e.None of the aboveQ6 Suppose the section manager from Information C is interested in the measures of central tendency and variation for the number of complaints which are handled well. Which of the following sets of values, where values are rounded to 3 decimal places, is the correct set of valuesa.Mean mu = 4.5 and variance sigma-squared = 1.125b.Mean mu = 4.5 and variance sigma-squared = 1.061c.Mean mu = 1.5 and variance sigma-squared = 1.125d.Mean mu = 1.5 and standard deviation sigma = 1.061e.None of the aboveInformation D, needed to answer Questions 7-9The manager of a large retailer thinks that one reason why staff at the complaints counter fail to handle customer complaints well is that not enough staff are allocated to this counter. Past experience has shown that the number of customers who arrive at this counter has a Poisson distribution where the average number who arrive each hour is 36. He decides to look at how many customers are likely to arrive at the complaints counter during a 5-minute period.Q7 Use Information D to answer this question. Which of the following statements concerning the probability that exactly 2 customers will arrive at the counter in a 5-minute period is correcta.less than 0.05b.between 0.21 and 0.23c.between 0.16 and 0.18d.more than 0.25e.None of the aboveQ8 Use Information D to answer this question. Which of the following statements concerning the probability that 3 or more customers will arrive at a counter in a 5-minute period is correcta.between 0.10 and 0.15b.less than 0.23c.more than 0.77d.between 0.60 and 0.55e.None of the aboveQ9 The section manager from Information D is interested in the mean and variance of the number of customers who arrive during a 1 hour period. Which of the following is the correct set of values for these two measuresa.Mean mu = 3 and variance sigma-squared = 3b.Mean mu = 36 and standard deviation sigma = 1.732c.Mean mu = 30 and variance sigma-squared = 30d.Mean mu = 36 and standard deviation sigma = 6e.None of the aboveTopic 5: Normal probability distribution & sampling distributionQ1 Which of the following is not a property of the normal distribution?a.It is bell-shaped.b.It is slightly skewed left.c.Its measures of central tendency are all identical.d.Its range is from negative infinity to positive infinity.Q2 The area under the standardized normal curve from 0 to 1.96 would be:a.the same as the area from 0 to -1.96.b.equal to 0.4750.c.found by using Table E.2 in your textbook.d.all of the above.Q3 Which of the following about the normal distribution is not true?a.Theoretically, the mean, median, and mode are the same.b.About two-thirds of the observations fall within ± 1 standard deviation from the mean.c.It is a discrete probability distribution.d.Its parameters are the mean and standard deviation.Q4 In its standardized form, the normal distribution:a.has a mean of 0 and a standard deviation of 1.b.has a mean of 1 and a variance of 0.c.has a total area equal to 0.5.d.cannot be used to approximate discrete binomial probability distributions.Q5 In the standardized normal distribution, the probability that Z > 0 is _______.a.0.00b.0.50c. 1.00d.cannot be found without more informationQ6 The probability of obtaining a value greater than 110 in a normal distribution in which the mean is 100 and the standard deviation is 10 is ______________ the probability of obtaining a value greater than 650 in a normal distribution with a mean of 500 and a standard deviation of 100.a.less thanb.equal to.c.greater thand.It is unknown without more information.Q7 The probability of getting a Z score greater than 4.0 is ________.a.close to 1.0b.0.50c. a negative numberd.almost zeroQ8 For some positive value of Z, the probability that a standardized normal variable is between 0 and Z is 0.3770. The value of Z isa.0.18b.0.81c. 1.16d. 1.47Q9 For some value of Z, the probability that a standardized normal variable is below Z is 0.2090. The value of Z isa.-0.81b.-0.31c.0.31d. 1.96Q10 Given that X is a normally distributed random variable with a mean of 50 and a standard deviation of 2, the probability that X is between 47 and 54 isa.0.0896b.0.4104c.0.5896d.0.9104Q11 For some positive value of X, the probability that a standardized normal variable is between 0 and +1.5X is 0.4332. The value of X isa.0.10b.0.50c. 1.00d. 1.50Q12 The owner of a fish market determined that the average weight for a catfish is 3.2 pounds with a standard deviation of 0.8 pounds. A citation catfish should be one of the top 2 percent in weight. Assuming the weights of catfish are normally distributed, at what weight (in pounds) should the citation designation be established?a. 1.56 poundsb. 4.84 poundsc. 5.20 poundsd.7.36 poundsQ13 Which of the following is NOT a property of the arithmetic mean?a.It is unbiased.b.It is always equal to the population mean.c.Its average is equal to the population mean.d.Its variance becomes smaller when the sample size gets bigger.Q14 The sampling distribution of the mean is a distribution of:a.individual population values.b.individual sample values.c.statistics.d.parameters.Q15 The standard deviation of the sampling distribution of the mean is called the:a.standard error of the sample.b.standard error of the estimate.c.standard error of the mean.d.All of the aboveQ16 According to the central limit theorem, the sampling distribution of the mean can be approximated by the normal distribution:a.as the number of samples gets "large enough."b.as the sample size (number of observations) gets "large enough."c.as the size of the population standard deviation increases.d.as the size of the sample standard deviation decreases.Q17 For a sample size of n=10, the sampling distribution of the mean will be normally distributed:a.regardless of the population's distribution.b.if the shape of the population is symmetrical.c.if the variance of the mean is known.d.if the population is normally distributedTopic 6: EstimationQ1 The interval estimate using the t critical value is ________ than the interval estimate using the z critical value.a.Narrowerb.The same asc.Widerd.More powerfulQ2 To estimate the mean of a normal population with unknown standard deviation using a small sample, we use the ______ distribution.a.'t'b.'Z'c.samplingd.alphaQ3 If the population does not follow a normal distribution, then to use the t distribution to give a confidence interval estimate for the population mean, the sample size should be:a.at least 5b.at least 30c.at least 100d.less than 30Q4 The 'z' value or 't' value used in the confidence interval formula is called the:a.sigma valueb.critical valuec.alpha valued.none of the aboveQ5 The 'z' value that is used to construct a 90 percent confident interval is:a. 1.645b. 1.96c. 2.33d. 2.58Q6 The 'z' value that is used to construct a 95 percent confidence interval is:a. 1.645b. 1.96c. 2.33d. 2.58Q7 The sample size needed to construct a 90 percent confidence interval estimate for the population mean with sampling error ±1.9 when sigma is known to be 10 units is:a.9b.32c.75d.107Q8 The t critical value approaches the z critical value when:a.the sample size decreasesb.the sample size approaches infinityc.the confidence level increasesd.the sample is smallQ9 The t-critical value used when constructing a 99 percent confidence interval estimate with a sample of size 18 is:a. 2.552b. 2.567c. 2.878d. 2.898Q10 The t-value that would be used to construct a 90 percent confidence interval for the mean with a sample of size n 36 would be:a. 1.3062b. 1.6499c. 1.6883d. 1.6896Q11 The value of alpha (two tailed) for a 96 percent confidence interval would be:a.0.02b.0.04c.0.2d.0.4Q12 When using the t distribution for confidence interval estimates for the mean, the degrees of freedom value is:a.nb.n-1c.n-2d.n %2B 1Q13 You would interpret a 90 percent confidence interval for the population mean as:a.you can be 90 percent confident that you have selected a sample whose interval doesinclude the population meanb.if all possible samples are selected and CI's are calculated, 90 percent of those intervalswould include the true population meanc.90 percent of the population is in that intervald.both A and B are trueQ14 From a sample of 100 items, 30 were defective. A 95 percent confidence interval for the proportion of defectives in the population is:a.(.2, .4)b.(.21, .39)c.(.225, .375)d.(.236, .364)Q15 A confidence interval was used to estimate the proportion of statistics students that are male.A random sample of 70 statistics students generated the following 90 percent confidence interval:(0.45, 0.64). Using the information above, what size sample would be necessary if we wanted to estimate the true proportion to within ±0.08 using 95 percent confidence?a.240b.450c.550d.150整理人：阿桤。

Solutions to End-of-Section and Chapter Review Problems 31CHAPTER 11.1 The type of beverage sold yields categorical or “qualitative” responses.The type of beverage sold yields distinct categories in which no ordering is implied.1.2 Three sizes of U.S. businesses are classified into distinct categories—small, medium, and large—in which order is implied.1.3 The time it takes to download a video from the Internet is a continuous numerical or“quantitative” variable because time can have any value from 0 to any reasonable unit of time.1.4 (a) The number of cellphones is a numerical variable that is discrete because the outcome isa count.(b) Monthly data usage is a numerical variable that is continuous because any value within arange of values can occur.(c) Number of text messages exchanged per month is a numerical variable that is discretebecause the outcome is a count.(d) Voice usage per month is a numerical variable that is continuous because any valuewithin a range of values can occur.(e) Whether a cellphone is used for email is a categorical variable because the answer can beonly yes or no.1.5 (a) numerical, continuous(b) numerical, discrete(c) categorical(d) categorical1.6 (a) Categorical(b) Numerical, continuous(c) Categorical(d) Numerical, discrete(e) Categorical1.7 (a) numerical, continuous *(b) categorical(c) categorical(d) numerical, discrete*Some researchers consider money as a discrete numerical variable because it can be “counted.”1.8 (a) numerical, continuous *(b) numerical, discrete(c) numerical, continuous *(d) categorical*Some researchers consider money as a discrete numerical variable because it can be “counted.”32 Chapter 1: Defining and Collecting Data1.9 (a) Income may be considered discrete if we “count” our money. It may be consideredcontinuous if we “measure” our money; we are only limited by the way a country'smonetary system treats its currency.(b) The first format is preferred because the responses represent data measured on a higherscale.1.10 The underlying variable, ability of the students, may be continuous, but the measuring device, thetest, does not have enough precision to distinguish between the two students.1.11 (a) The population is “all working women from the metropolitan area.” A systematic or randomsample could be taken of women from the metropolitan area. The director might wish tocollect both numerical and categorical data.(b) Three categorical questions might be occupation, marital status, type of clothing.Numerical questions might be age, average monthly hours shopping for clothing, income.1.12 The answer depends on the chosen data set.1.13 The answer depends on the specific story.1.14 The answer depends on the specific story.1.15 The transportation engineers and planners should use primary data collected through anobservational study of the driving characteristics of drivers over the course of a month.1.16 The information presented there is based mainly on a mixture of data distributed by anorganization and data collected by ongoing business activities.1.17 (a) 001 (b) 040 (c) 9021.18 Sample without replacement: Read from left to right in 3-digit sequences and continue unfinishedsequences from end of row to beginning of next row.Row 05: 338 505 855 551 438 855 077 186 579 488 767 833 170Rows 05-06: 897Row 06: 340 033 648 847 204 334 639 193 639 411 095 924Rows 06-07: 707Row 07: 054 329 776 100 871 007 255 980 646 886 823 920 461Row 08: 893 829 380 900 796 959 453 410 181 277 660 908 887Rows 08-09: 237Row 09: 818 721 426 714 050 785 223 801 670 353 362 449Rows 09-10: 406Note: All sequences above 902 and duplicates are discarded.1.19 (a) Row 29: 12 47 83 76 22 99 65 93 10 65 83 61 36 98 89 58 86 92 71Note: All sequences above 93 and all repeating sequences are discarded.(b) Row 29: 12 47 83 76 22 99 65 93 10 65 83 61 36 98 89 58 86Note: All sequences above 93 are discarded. Elements 65 and 83 are repeated.Solutions to End-of-Section and Chapter Review Problems 33 1.20 A simple random sample would be less practical for personal interviews because of travel costs(unless interviewees are paid to attend a central interviewing location).1.21 This is a probability sample because the selection is based on chance. It is not a simple randomsample because A is more likely to be selected than B or C.1.22 Here all members of the population are equally likely to be selected and the sample selectionmechanism is based on chance. But not every sample of size 2 has the same chance ofbeing selected. For example the sample “B and C” is impossible.1.23 (a) Since a complete roster of full-time students exists, a simple random sample of 200students could be taken. If student satisfaction with the quality of campus life randomlyfluctuates across the student body, a systematic 1-in-20 sample could also be taken fromthe population frame. If student satisfaction with the quality of life may differ by genderand by experience/class level, a stratified sample using eight strata, female freshmenthrough female seniors and male freshmen through male seniors, could be selected. Ifstudent satisfaction with the quality of life is thought to fluctuate as much within clustersas between them, a cluster sample could be taken.(b) A simple random sample is one of the simplest to select. The population frame is theregistrar’s file of 4,000 student names.(c) A systematic sample is easier to select by hand from the registrar’s records than asimple random sample, since an initial person at random is selected and then every 20thperson thereafter would be sampled. The systematic sample would have the additionalbenefit that the alphabetic distribution of sampled students’ names would be morecomparable to the alphabetic distribution of student names in the campus population.(d) If rosters by gender and class designations are readily available, a stratified sampleshould be taken. Since student satisfaction with the quality of life may indeed differ bygender and class level, the use of a stratified sampling design will not only ensure allstrata are represented in the sample, it will also generate a more representative sampleand produce estimates of the population parameter that have greater precision.(e) If all 4,000 full-time students reside in one of 10 on-campus residence halls which fullyintegrate students by gender and by class, a cluster sample should be taken. A clustercould be defined as an entire residence hall, and the students of a single randomlyselected residence hall could be sampled. Since each dormitory has 400 students, asystematic sample of 200 students can then be selected from the chosen cluster of 400students. Alternately, a cluster could be defined as a floor of one of the 10 dormitories.Suppose there are four floors in each dormitory with 100 students on each floor. Twofloors could be randomly sampled to produce the required 200 student sample. Selectionof an entire dormitory may make distribution and collection of the survey easier toaccomplish. In contrast, if there is some variable other than gender or class that differsacross dormitories, sampling by floor may produce a more representative sample.34 Chapter 1: Defining and Collecting Data1.24 (a) Row 16: 2323 6737 5131 8888 1718 0654 6832 4647 6510 4877Row 17: 4579 4269 2615 1308 2455 7830 5550 5852 5514 7182Row 18: 0989 3205 0514 2256 8514 4642 7567 8896 2977 8822Row 19: 5438 2745 9891 4991 4523 6847 9276 8646 1628 3554Row 20: 9475 0899 2337 0892 0048 8033 6945 9826 9403 6858Row 21: 7029 7341 3553 1403 3340 4205 0823 4144 1048 2949Row 22: 8515 7479 5432 9792 6575 5760 0408 8112 2507 3742Row 23: 1110 0023 4012 8607 4697 9664 4894 3928 7072 5815Row 24: 3687 1507 7530 5925 7143 1738 1688 5625 8533 5041Row 25: 2391 3483 5763 3081 6090 5169 0546Note: All sequences above 5000 are discarded. There were no repeating sequences.(b) 089 189 289 389 489 589 689 789 889 9891089 1189 1289 1389 1489 1589 1689 1789 1889 19892089 2189 2289 2389 2489 2589 2689 2789 2889 29893089 3189 3289 3389 3489 3589 3689 3789 3889 39894089 4189 4289 4389 4489 4589 4689 4789 4889 4989(c) With the single exception of invoice #0989, the invoices selected in the simplerandom sample are not the same as those selected in the systematic sample. It would behighly unlikely that a random process would select the same units as a systematicprocess.1.25 (a) A stratified sample should be taken so that each of the three strata will be proportionatelyrepresented.(b) The number of observations in each of the three strata out of the total of 1,000 shouldreflect the proportion of the three categories in the customer database. For example,3,500/10,000 = 35% so 35% of 1,000 = 350 customers should be selected from theprospective buyers; similarly 4,500/10,000 = 45% so 450 customers should be selectedfrom the first time buyers, and 2,000/10,000 = 20% so 200 customers from the repeatbuyers.(c) It is not simple random sampling because, unlike the simple random sampling, it ensuresproportionate representation across the entire population.1.26 Before accepting the results of a survey of college students, you might want to know, forexample:Who funded the survey? Why was it conducted? What was the population from which the sample was selected? What sampling design was used? What mode of response was used: a personalinterview, a telephone interview, or a mail survey? Were interviewers trained? Were surveyquestions field-tested? What questions were asked? Were they clear, accurate, unbiased, valid?What operational definition of “vast majority” was used? What was the response rate? What was the sample size?1.27 (a) Possible coverage error: Only employees in a specific division of the company weresampled.(b) Possible nonresponse error: No attempt is made to contact nonrespondents to urge themto complete the evaluation of job satisfaction.(c) Possible sampling error: The sample statistics obtained from the sample will not be equalto the parameters of interest in the population.(d) Possible measurement error: Ambiguous wording in questions asked on thequestionnaire.Solutions to End-of-Section and Chapter Review Problems 35 1.28 The results are based on an online survey. If the frame is supposed to be small business owners,how is the population defined? This is a self-selecting sample of people who responded online, so there is an undefined nonresponse error. Sampling error cannot be determined since this is not a random sample.1.29 Before accepting the results of the survey, you might want to know, for example:Who funded the study? Why was it conducted? What was the population from which the sample was selected? What was the frame being used? What sampling design was used?What mode of response was used: a personal interview, a telephone interview, or a mail survey?Were interviewers trained? Were survey questions field-tested? What other questions wereasked? Were they clear, accurate, unbiased, and valid? What was the response rate? What was the margin of error? What was the sample size?1.30 Before accepting the results of the survey, you might want to know, for example: Who funded thestudy? Why was it conducted? What was the population from which the sample was selected?What sampling design was used? What mode of response was used: a personal interview, atelephone interview, or a mail survey? Were interviewers trained? Were survey questions field-tested? What other questions were asked? Were the questions clear, accurate, unbiased, andvalid? What was the response rate? What was the margin of error? What was the sample size?What frame was used?1.31 A population contains all the items of interest whereas a sample contains only a portion of theitems in the population.1.32 A statistic is a summary measure describing a sample whereas a parameter is a summary measuredescribing an entire population.1.33 Categorical random variables yield categorical responses such as yes or no answers. Numericalrandom variables yield numerical responses such as your height in inches.1.34 Discrete random variables produce numerical responses that arise from a counting process.Continuous random variables produce numerical responses that arise from a measuring process.1.35 Items or individuals in a probability sampling are selected based on known probabilities whileitems or individuals in a nonprobability samplings are selected without knowing theirprobabilities of selection.1.36 Microsoft Excel could be used to perform various statistical computations that were possible onlywith a slide-rule or hand-held calculator in the old days.1.37 (a) The population of interest was 18-54 year olds who currently own a smartphone and/ortablet, and who use and do not use these devices to shop.(b) The sample was the 1,003 18-54 year olds who currently own a smartphone and/or tablet,who use and do not use these devices to shop, and who responded to the study.(c) A parameter of interest is the proportion of all tablet users in the population who use theirdevice to purchase product and services.(d) A statistic used to estimate the parameter of interest in (c) is the proportion of tablet usersin the sample who use their device to purchase product and services.36 Chapter 1: Defining and Collecting Data1.38 The answers to this question depend on which article and its corresponding data set is beingselected.1.39 (a) The population of interest was supply chain executives in a wide range of industriesrepresenting a mix of company sizes from across three global regions: Asia, Europe, andthe Americas.(b) The sample was the 503 supply chain executives in a wide range of industriesrepresenting a mix of company sizes from across three global regions: Asia, Europe, andthe Americas surveyed by PwC from May to July 2012.(c) A parameter of interest is the proportion of supply chain executives in the populationwho acknowledge that supply chain is seen as a strategic asset in their company.(d) A statistic used to estimate the parameter of interest in (c) is the proportion of supplychain executives in the sample who acknowledge that supply chain is seen as a strategicasset in their company.1.40 The answers to this question depend on which data set is being selected.1.41 (a) Categorical variable: Which of the following best describes this firm’s primary business?(b) Numerical variable: On average, what percent of total monthly revenues are e-commercerevenues?1.42 (a) The population of interest was the collection of all the 10,000 benefitted employees at theUniversity of Utah when the study was conducted.(b) The sample consisted of the 3,095 benefitted employees participated in the study.(c) gender: categorical; age: numerical; education level: numerical; marital status:categorical; household income: numerical; employment category: categorical1.43 (a) (i)categorical (iii) numerical, discrete(ii)categorical (iv) categorical(b) The answers will vary.(c) The answers will vary.。