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STA 291 Fall 2009 PowerPoint PPT Presentation

STA 291 Fall 2009. Lecture 21 Dustin Lueker. Example. If the null hypothesis is rejected at a 2% level of significance, will the null be rejected at a 5% level of significance? Yes No Maybe. Example.

STA 291 Fall 2009

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STA 291Fall 2009

Lecture 21

Dustin Lueker

Example

• If the null hypothesis is rejected at a 2% level of significance, will the null be rejected at a 5% level of significance?

• Yes

• No

• Maybe

STA 291 Fall 2009 Lecture 21

Example

• If the null hypothesis is rejected at a 2% level of significance, will the null be rejected at a 1% level of significance?

• Yes

• No

• Maybe

STA 291 Fall 2009 Lecture 21

Test Statistic

• Testing µ

• Without the aide of some type of technology it is impossible to find exact p-values when using this test statistic, because it is from the t-distribution

STA 291 Fall 2009 Lecture 21

Testing the Difference Between Means from Different Populations

• Hypothesis involves 2 parameters from 2 populations

• Test statistic is different

• Involves 2 large samples (both samples at least 30)

• One from each population

• H0: μ1-μ2=0

• Same as H0: μ1=μ2

• Test statistic

STA 291 Fall 2009 Lecture 21

Example

• In the 1982 General Social Survey, 350 subjects reported the time spend every day watching television. The sample yielded a mean of 4.1 and a standard deviation of 3.3.

• In the 1994 survey, 1965 subjects yielded a sample mean of 2.8 hours with a standard deviation of 2.

• Set up hypotheses of a significance test to analyze whether the population means differ in 1982 and 1994 and test at α=.05 using the p-value method.

STA 291 Fall 2009 Lecture 21

Small Sample Tests for Two Means

• Used when comparing means of two samples where at least one of them is less than 30

• Normal population distribution is assumed for both samples

• Equal Variances

• Both groups have the same variability

• Unequal Variances

• Both groups may not have the same variability

STA 291 Fall 2009 Lecture 21

Small Sample Test for Two Means, Equal Variances

• Test Statistic

• Degrees of freedom

• n1+n2-2

STA 291 Fall 2009 Lecture 21

Small Sample Confidence Interval for Two Means, Equal Variances

• Degrees of freedom

• n1+n2-2

STA 291 Fall 2009 Lecture 21

Small Sample Test for Two Means, Unequal Variances

• Test statistic

• Degrees of freedom

STA 291 Fall 2009 Lecture 21

Small Sample Confidence Interval for Two Means, Unequal Variances

STA 291 Fall 2009 Lecture 21

Method 1 (Equal Variances) vs. Method 2 (Unequal Variances)

• How to choose between Method 1 and Method 2?

• Method 2 is always safer to use

• Definitely use Method 2

• If one standard deviation is at least twice the other

• If the standard deviation is larger for the sample with the smaller sample size

• Usually, both methods yield similar conclusions

STA 291 Fall 2009 Lecture 21