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统计学要点摘要英文版-Statistic-Review

统计学要点摘要英文版-Statistic-Review

Chapter 2 Statistic ReviewA.Random variables；1.expected value:Define ：X is a discrete random variable, “ the mean (or expected value）of X " is the weighted average of the possible outcomes, where the probabilities of the outcomeserve as the appropriate weight.p i is ith of prob.，i=1，2, ……nInterpretation：The random variable is a variable that have a probability associated with each outcome. Outcome is not controlled。

Discrete random Var。

: has finite outcome，or outcome is countable infinite.Continuous random Var。

：uncountable infinite outcome，the probability of each outcome is small because of too many numbers.For normal random Var。

, probability density function is used to calculate the probability between the are.E( )：the expectations operator，→… “ sample mean”, used to estimateThe is changed from sample to sample. is not a fixed on time，the outcome selected should not be the same. There is prob。

Ch10 Hypothesis Testing, One Population Mean or Proportion 商务统计学概论(英文第四版)教学课件 Introd

Ch10 Hypothesis Testing, One Population Mean or Proportion 商务统计学概论(英文第四版)教学课件 Introd

The Logic of Hypothesis Testing
• Step 5. • The decision is a conclusion supported
Make
by evidence. The decision maker will:
the decision.
– reject the null hypothesis if the sample evidence is so strong, the sample statistic so unlikely, that the decision maker is
• Type II Error:
– Saying you do not reject H0 when it really is false.
– Failing to reject a false H0.
© 2002 The Wadsworth Group
Acceptable Error for the Example
decision for there some action triggered, some
future
change implied? What

actions?
recommendations might be
extended for future attempts to
test similar hypotheses?
– Not in adjustment - H1: µ 1.3250 minutes
© 2002 The Wadsworth Group
Types of Error
Test Says
H0 True
H0 False

Chapter 3 Probability Statistics 统计学 英文教材

Chapter 3 Probability Statistics 统计学 英文教材

Event: { Die is even }={ 2 4 6 }
A subset of the sample space.
Outcome:
Larson/Farber Ch. 3
{4} The result of a single trial
3
Another Experiment
Probability Experiment: An action through which
= 400 / 1000 = 0.4 = 450 / 1000 = 0.45 =250 / 1000 = 0.25 = 95 / 250 = 0.38 Answers: 1) 0.4 2) 0.45 3) 0.25 4) 0.38
Larson/Farber Ch. 3 15
Miami 150 95 5 250
Empirical
P(E) = Frequency Total of event Frequency E
Probability blood pressure will decrease after medication
Intuition
Probability the line will be busy
9
Conditional Probability
The probability an event B will occur, given (on the condition) that another event A has occurred.
We write this as P(B|A) and say “probability of B, given A”.
{1, 2, 3, 4, 5, 6}
The conditional probability, P(B|A) = 1/6

统计学第十章

统计学第十章

14
Testing for a Population Mean with a Known Population Standard Deviation- Example
Step 1: State the null hypothesis and the alternate hypothesis.
H0: µ = 200 H1: µ ≠ 200
7
Left-tail or Right-tail Test?
• The direction of the test involving claims that use the words “has improved”, “is better than”, and the like will depend upon the variable being measured. • For instance, if the variable involves time for a certain medication to take effect, the words “better” “improve” or more effective” are translated as “<” (less than, i.e. faster relief). • On the other hand, if the variable refers to a test score, then the words “better” “improve” or more effective” are translated as “>” (greater than, i.e. higher test scores)
Jamestown Steel Company manufactures and assembles desks and other office equipment at several plants in western New York State. The weekly production of the Model A325 desk at the Fredonia Plant follows the normal probability distribution with a mean of 200 and a standard deviation of 16. Recently, because of market expansion, new production methods have been introduced and new employees hired. The vice president of manufacturing would like to investigate whether there has been a change in the weekly production of the Model A325 desk.

英文商务统计学ppt_第10章Ch10

英文商务统计学ppt_第10章Ch10
Mean 1 vs. Mean 2
Population Means, Related Samples
Same group before vs. after treatment
Population Proportions
Population Variances
Proportion 1 vs. Proportion 2
Variance 1 vs. Variance 2
Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc.
Chap 10-3
Difference Between Two Means
Population means, independent samples
Chap 10-5
Hypothesis Tests for Two Population Means
Two Population Means, Independent Samples Lower-tail test: Upper-tail test: Two-tail test:
H0: μ1 μ2 H1: μ1 < μ2

DPopulation means, independent samples
*
Unrelated Independent

Sample selected from one population has no effect on the sample selected from the other population
The means of two related populations
The proportions of two independent populations The variances of two independent populations

统计学(中英文)_ch01

统计学(中英文)_ch01

Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 1-12
∑X
n
i
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 1-8
Inferential Statistics 推断统计
Estimation 估计 e.g., Estimate the population mean weight using the sample mean weight 例如：利用采样的平均重量估计人口的平均体 重 Hypothesis testing 假设检验 e.g., Test the claim that the population mean weight is 120 pounds 例如：根据测试的要求，人口平均体重是120 磅
英文翻译乃自己所做， 英文翻译乃自己所做，有错误 之处请自行查证。 之处请自行查证。
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 1-1
Business Statistics, A First Course
Defined descriptive vs. inferential statistics 描述性统计和推理统计 Reviewed data types 回顾数据类型
♦ ♦ ♦ ♦
Categorical vs. Numerical data 绝对的和数值的数据 Discrete vs. Continuous data 离散的和连续的数据

ch10 Time Series Data 《计量经济学导论》课件


Economics 20 - Prof. Anderson
8
Variances of OLS Estimators
Just as in the cross-section case, we need to add an assumption of homoskedasticity in order to be able to derive variances
Economics 20 - Prof. Anderson
7
Unbiasedness of OLS
Based on these 3 assumptions, when using time-series data, the OLS estimators are unbiased Thus, just as was the case with crosssection data, under the appropriate conditions OLS is unbiased Omitted variable bias can be analyzed in the same manner as in the cross-section case
Contemporaneous exogeneity will only be sufficient in large samples
Economics 20 - Prof. Anderson
6
Assumptions (continued)
Still need to assume that no x is constant, and that there is no perfect collinearity
Note we have skipped the assumption of a random sample

CH10 Statistical charts and tables Medical Statistics医学统计学 教学课件


Table 10-3 compare of the risk factor of patients
They can show the information of data directly. So they are widely used in medical practice.
§1 Statistical Tables
Principles of Making Tables
The main contents must be emphasized, simple and understood easily. Primary and secondary contents as well as arrangement must be clear.
2. Combinative table: More than 2 variables
Table 10-2 the result of HBsAg of persons at different age group in city or country at certain area in certain year
city
Number of pe Number of persons group
rsons tested with positive result
<20
42384
274
20~
228076
2018
25~
235879
2697
30~
146142
2093
35~
74629
1299
40
21193
273
tatal
Chapter 10
Statistical Table &Statistical Graph

基础统计学英文课件 (10)


In Symbols
State H0 and Ha.
Identify .
n = total number of + and – signs
Performing The Paired-Sample Sign Test
In Words
4. Determine the critical value.
z (40 0.5) 0.5(100) 1.9 100 2
• Decision: Fail to Reject H0
At the 1% level of significance you cannot reject the dealership’s claim.
The Paired-Sample Sign Test
775 765 801 742 754 753 739 751 745 750 777 769 756 760 782 789
Solution: Using the Sign Test
• H0: median ≤ 750 • Ha: median > 750
• Compare each data entry with the hypothesized median 750
• Right-tailed test: H0: median k and Ha: median > k
• Two-tailed test: H0: median = k and Ha: median k
Sign Test for a Population Median
• To use the sign test, each entry is compared with the hypothesized median k. § If the entry is below the median, a sign is assigned. § If the entry is above the median, a + sign is assigned. § If the entry is equal to the median, 0 is assigned.

统计学英文版教材课件

For example, A ∪ B = {1, 3, 4, 5}.
S A 1 5 2
STAT7055 - Lecture 2
B 3 4
6
February 17, 2016 13 / 64
Introduction
Intersection, Union and Complement
Complement
STAT7055 LECTURE 2 Probability
பைடு நூலகம்
February 17, 2016
STAT7055 - Lecture 2
February 17, 2016
1 / 64
Introduction
Definitions
Random Experiment
A random experiment is a process that results in one of several possible outcomes, none of which can be predicted with certainty. For example:
STAT7055 - Lecture 2
February 17, 2016
7 / 64
Introduction
Events
Events
A simple event is an individual outcome from the sample space. An event is a collection of one or more simple events (or outcomes).
STAT7055 - Lecture 2
February 17, 2016
3 / 64
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We saw earlier that point probabilities in continuous distributions were virtually zero. Likewise, we’d expect that the point estimator gets closer to the parameter value with an increased sample size, but point estimators don’t reflect the effects of larger sample sizes. Hence we will employ the interval estimator to estimate population parameters…
Copyright © 2009 Cengage Learning
Unbiased Estimators…
An unbiased estimator of a population parameter is an estimator whose expected value is equal to that parameter. E.g. the sample median is an unbiased estimator of the population mean µ since: E(Sample median) = µ
To do so we need the population parameters. Binomial: p Poisson: µ Normal: µ and σ Exponential: λ or µ
Cop we have been…
Copyright © 2009 Cengage Learning
Consistency…
An unbiased estimator is said to be consistent if the difference between the estimator and the parameter grows smaller as the sample size grows larger. E.g. X is a consistent estimator of µ because: V(X) is σ2/n That is, as n grows larger, the variance of X grows smaller.
Qualities desirable in estimators include unbiasedness, consistency, and relative efficiency: An unbiased estimator of a population parameter is an estimator whose expected value is equal to that parameter. An unbiased estimator is said to be consistent if the difference between the estimator and the parameter grows smaller as the sample size grows larger. If there are two unbiased estimators of a parameter, the one whose variance is smaller is said to be relatively efficient.
Copyright © 2009 Cengage Learning
Interval Estimator…
An interval estimator draws inferences about a population by estimating the value of an unknown parameter using an interval.
Copyright © 2009 Cengage Learning
Consistency…
An unbiased estimator is said to be consistent if the difference between the estimator and the parameter grows smaller as the sample size grows larger. E.g. Sample median is a consistent estimator of µ because: V(Sample median) is 1.57σ2/n That is, as n grows larger, the variance of the sample median grows smaller.
Chapter 10
Introduction to Estimation
Copyright © 2009 Cengage Learning
Where we have been…
Chapter 7 and 8: Binomial, Poisson, normal, and exponential distributions allow us to make probability statements about X (a member of the population).
That is we say (with some ___% certainty) that the population parameter of interest is between some lower and upper bounds.
Copyright © 2009 Cengage Learning
Point & Interval Estimation…
For example, suppose we want to estimate the mean summer income of a class of business students. For n = 25 students, is calculated to be 400 $/week.
Statistics Data Information
Population
Sample
Inference
Statistic Parameter
In order to do inference, we require the skills and knowledge of descriptive statistics, probability distributions, and sampling distributions.
Chapter 9: Sampling distributions allow us to make probability statements about statistics. We need the population parameters. Sample mean: µ and σ Sample proportion: p Difference between sample means: µ1,σ1 ,µ , and σ2 2
Copyright © 2009 Cengage Learning
Estimation…
The objective of estimation is to determine the approximate value of a population parameter on the basis of a sample statistic. There are two types of estimators: Point Estimator Interval Estimator
Copyright © 2009 Cengage Learning
Unbiased Estimators…
An unbiased estimator of a population parameter is an estimator whose expected value is equal to that parameter. E.g. the sample mean X is an unbiased estimator of the population mean µ , since: E(X) = µ
Copyright © 2009 Cengage Learning
Estimation…
There are two types of inference: estimation and hypothesis testing; estimation is introduced first. The objective of estimation is to determine the approximate value of a population parameter on the basis of a sample statistic. E.g., the sample mean ( population mean ( ). ) is employed to estimate the
Copyright © 2009 Cengage Learning
Where we are going…
However, in almost all realistic situations parameters are unknown. We will use the sampling distribution to draw inferences about the unknown population parameters.
Copyright © 2009 Cengage Learning
Point Estimator…