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统计重点整理CH10-Analyzing the Differences in Two Populations

Chapter 10: Analyzing the Differences in Two Populations Hypothesis Testing :

Confidence Intervals - Difference in Means using z Statistic (Population Variance Known)

The central limit theorem states that the difference in two sample means is normally distributed

统计重点整理CH10-Analyzing the Differences in Two Populations

统计重点整理CH10-Analyzing the Differences in Two Populations

统计重点整理CH10-Analyzing the Differences in Two Populations

Confidence Interval

统计重点整理CH10-Analyzing the Differences in Two Populations

Sometimes the solution(s) is/are to take a random sample from each of the two populations and study the difference in the two samples

统计重点整理CH10-Analyzing the Differences in Two Populations

Formula for confidence interval to estimate (μ1 - μ2)

统计重点整理CH10-Analyzing the Differences in Two Populations

统计重点整理CH10-Analyzing the Differences in Two Populations

统计重点整理CH10-Analyzing the Differences in Two Populations

统计重点整理CH10-Analyzing the Differences in Two Populations

统计重点整理CH10-Analyzing the Differences in Two Populations

统计重点整理CH10-Analyzing the Differences in Two Populations

t Each of the two populations is normally distributed . The two samples are independent . The values of the population variances are unknown .

统计重点整理CH10-Analyzing the Differences in Two Populations

The variances of the two populations are equal. σ12 =σ

22

统计重点整理CH10-Analyzing the Differences in Two Populations

统计重点整理CH10-Analyzing the Differences in Two Populations

统计重点整理CH10-Analyzing the Differences in Two Populations

统计重点整理CH10-Analyzing the Differences in Two Populations

2 2s 12 = s 22

Dependent samples

统计重点整理CH10-Analyzing the Differences in Two Populations

Used in before and after studies

统计重点整理CH10-Analyzing the Differences in Two Populations

统计重点整理CH10-Analyzing the Differences in Two Populations

After measurement is not independent of the before measurement Researcher must determine if the two samples are related to each other

统计重点整理CH10-Analyzing the Differences in Two Populations

The technique for related samples is different from the technique used to analyze independent samples

统计重点整理CH10-Analyzing the Differences in Two Populations

Matched pairs test requires the two samples be the same size

统计重点整理CH10-Analyzing the Differences in Two Populations

The following t

统计重点整理CH10-Analyzing the Differences in Two Populations

test for dependent measures uses the sample difference, d , between individual matched samples as the basic measurement of analysis

统计重点整理CH10-Analyzing the Differences in Two Populations

统计重点整理CH10-Analyzing the Differences in Two Populations

统计重点整理CH10-Analyzing the Differences in Two Populations

统计重点整理CH10-Analyzing the Differences in Two Populations

统计重点整理CH10-Analyzing the Differences in Two Populations

An analysis of d converts the problem from a two sample problem to a single sample of differences Formulas for Dependent Samples

If σ is unknown, it can be estimated by pooling the two sample variances and computing a pooled sample standard deviation

p

?1

统计重点整理CH10-Analyzing the Differences in Two Populations

p

?2

统计重点整理CH10-Analyzing the Differences in Two Populations

统计重点整理CH10-Analyzing the Differences in Two Populations

Confidence Intervals

Researcher can be interested in estimating the mean difference in two populations for related samples

统计重点整理CH10-Analyzing the Differences in Two Populations

This requires a confidence interval of D (the mean population difference of two related

samples) to be constructed

Confidence Intervals for Mean Difference for Related Samples

Sample proportion is used ( – )

Sampling Distribution of Differences in Sample Proportions

统计重点整理CH10-Analyzing the Differences in Two Populations

统计重点整理CH10-Analyzing the Differences in Two Populations

统计重点整理CH10-Analyzing the Differences in Two Populations

统计重点整理CH10-Analyzing the Differences in Two Populations

统计重点整理CH10-Analyzing the Differences in Two Populations

统计重点整理CH10-Analyzing the Differences in Two Populations

统计重点整理CH10-Analyzing the Differences in Two Populations

统计重点整理CH10-Analyzing the Differences in Two Populations

统计重点整理CH10-Analyzing the Differences in Two Populations

统计重点整理CH10-Analyzing the Differences in Two Populations

Z Formula to Test the Difference in Population Proportions

Z Formula for the Difference in Two Population Proportions

Confidence Interval to Estimate p 1 - p 2