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STA 291 Fall 2009

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 291 Fall 2009

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  1. STA 291Fall 2009 Lecture 21 Dustin Lueker

  2. 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

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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

  8. Small Sample Test for Two Means, Equal Variances • Test Statistic • Degrees of freedom • n1+n2-2 STA 291 Fall 2009 Lecture 21

  9. Small Sample Confidence Interval for Two Means, Equal Variances • Degrees of freedom • n1+n2-2 STA 291 Fall 2009 Lecture 21

  10. Small Sample Test for Two Means, Unequal Variances • Test statistic • Degrees of freedom STA 291 Fall 2009 Lecture 21

  11. Small Sample Confidence Interval for Two Means, Unequal Variances STA 291 Fall 2009 Lecture 21

  12. 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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