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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

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