STA 291 Fall 2009

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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.

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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

• 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

• 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

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