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THE AUSTRALIAN NATIONAL UNIVERSITY SCHOOL OF FINANCE AND APPLIED STATISTICS

PRACTICE/MOCK Second Semester Final Examination 2011

FINANCIAL STATISTICS (STAT7055)

Writing Period: 3 hours duration Study Period: 15 minutes duration Permitted Material: Non-programmable calculator, dictionary and one A4 page with notes on both sides

Total Marks: 115

Instructions to Candidates: ·Attempt ALL questions. ·Start your solution to each question on a new page. ·To ensure full marks show all the steps in working out your solution. Marks may be deducted for failure to show appropriate calculations or formulae. ·Unless otherwise stated, give all answers to 3 decimal places. ·Selected statistical tables are attached to the back of the examination paper. Question 1[20 marks] (a) Michelle has heard that, “The average grade for STAT7055 is never above 75%”. She would like to test this claim.

i. [2 marks]State the null and alternative hypotheses. ii.[4 marks]Suppose she samples 8 students and calculates the mean of their final grade to be 77% and the sample standard deviation to be 6%. What is the outcome of the test at the 5% significance level? Calculate the p-value to test Michelle’s claim.

In another subject (FINM7006), Michelle’s tutor claims that the average score for the final exam is 70%. She has her suspicions, as all her friends either performed very poorly or very well in the exam. Michelle has yet to meet anyone who achieved a grade close to 70%. Using a sample of 5 randomly surveyed FIMN7006 students, Michelle found the sample mean to be 75%. Suppose the population standard deviation known to be 10%.

i. [4 marks]Test whether the average grade for the final exam of FINM7006 is equal to 70% at the 10% significance level.

ii. [6 marks]The lecturer tells you that the average grade was in fact 72%. What is the probability of a Type II error?

iii. [4 marks]What is the power of the test? What is the relation between the power of the test and the distance between the hypothesised value and the real value of the population mean?

Question 2[20 marks] (a) Newspapers are concerned about falling readership, in particular among members of so called “Gen Y” – those born between the early 1980s and late 1990s. One particular market research project is examining different rates of readership among university students studying in different areas. 100 undergraduates who are majoring in Arts and Social Sciences are interviewed, along with 100 students majoring in Engineering and Computer Science, with the main question asked being “How many times per week do you read a daily newspaper?” From the Arts students an average of 5.6 times per week is obtained, with standard deviation of 2.0, while the Engineering students give an average of 4.5 times per week with a standard deviation of 1.8.

i. [5 marks]Test the assumption that the variances of the populations of newspaper reading for the different groups are the same. Use a 10% significance level.

ii. [7 marks]Perform a formal hypothesis test to determine if the data suggest that Arts students have higher true mean newspaper readership than Engineering students. Be careful to state all assumptions, checking as appropriate, and use a significance level of 1%.

(b) A different study into newspaper readership was undertaken using a telephone poll. 85 people in a major metropolitan city were questioned, and if was found that 55 of them purchased a newspaper at least once a week. 90 people from a rural area were interviewed and it was found that 68 of them purchased a newspaper at least once a week.

i. [3 marks] Does this study involve independent samples? Briefly explain your answer.

ii. [5 marks] It is suspected that the true proportion of people who live in rural areas who purchase a newspaper at least once per week is higher than the corresponding proportion among metropolitan dwellers. Test if this suspicion is supported by the data.

Question 3[30 marks]

(a) David has just finished his first semester of teaching STAT7055. He is keen to analyse the teaching evaluations of his students. Students ranked David’s teaching abilities on a scale of 1 (poor) to 10 (excellent). Moreover, David feels his teaching evaluation from a student is dependent on whether the student attended his Monday or Wednesday lecture.

David has tabulated the following data using a random sample of his students surveyed: