STA 291 Spring 2008 Lecture 20 Dustin Lueker

Example A 95% confidence interval for µ is (96,110). Which of the following statements about significance tests for the same data is true? When testing H1: μ≠100, p-value>.05 When testing H1: μ≠100, p-value<.05 STA 291 Spring 2008 Lecture 20

Test Statistic Testing µ with σ unknown and n small Just like finding a confidence interval for µ with σ unknown and n small Reasons for choosing test statistics are the same as choosing the correct confidence interval formula Note: It is difficult for us to find p-values for this test statistic because of the way our table is set up STA 291 Spring 2008 Lecture 20

Correlation Between Tests and Confidence Intervals Results of confidence intervals and of two- sided significance tests are consistent Whenever the hypothesized mean is not in the confidence interval around the sample mean, then the p-value for testing H0: μ=μ0 is smaller than 5% (significance at the 5% level) In general, a 100(1-α)% confidence interval corresponds to a test at significance level α STA 291 Spring 2008 Lecture 20

Significance Test for a Proportion Same process as with population mean Value we are testing against is called p0 Test statistic P-value Calculation is exactly the same as for the test for a mean STA 291 Spring 2008 Lecture 20

Example Let p denote the proportion of Floridians who think that government environmental regulations are too strict A telephone poll of 824 people conducted in June 1995 revealed that 26.6% said regulations were too strict Test H0: p=.5 at α=.05 Calculate the test statistic Find the p-value and interpret Construct a 95% confidence interval. What is the advantage of the confidence interval over the test STA 291 Spring 2008 Lecture 20

Testing Difference Between Two Population Proportions Similar to testing one proportion Hypotheses are set up like two sample mean test H0:p1=p2 Same as H0:p1-p2=0 Test Statistic STA 291 Spring 2008 Lecture 20

Example Government agencies have undertaken surveys of Americans 12 years of age and older. Each was asked whether he or she used drugs at least once in the past month. The results of this year’s survey had 171 yes responses out of 306 surveyed while the survey 10 years ago resulted in 158 yes responses out of 304 surveyed. Test whether the use of drugs in the past ten years has increased. State and test the hypotheses using the rejection region method at the 8% level of significance. STA 291 Spring 2008 Lecture 20