Lecture 19 Dustin Lueker.  A 95% confidence interval for µ is (96,110). Which of the following statements about significance tests for the same data.

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Lecture 19 Dustin Lueker

 A 95% confidence interval for µ is (96,110). Which of the following statements about significance tests for the same data is true? 1.When testing H 1 : μ≠100, p-value>.05 2.When testing H 1 : μ≠100, p-value<.05 STA 291 Summer 2010 Lecture 192

 Testing µ with n small ◦ Just like finding a confidence interval for µ 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 3STA 291 Summer 2010 Lecture 19

 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 H 0 : μ=μ 0 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 4STA 291 Summer 2010 Lecture 19

 Same process as with population mean  Value we are testing against is called p 0  Test statistic  P-value ◦ Calculation is exactly the same as for the test for a mean  Sample size restrictions: 5STA 291 Summer 2010 Lecture 19

 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 2005 revealed that 26.6% said regulations were too strict ◦ Test H 0 : 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 6STA 291 Summer 2010 Lecture 19

 Similar to testing one proportion  Hypotheses are set up like two sample mean test ◦ H 0 :p 1 =p 2  Same as H 0 :p 1 -p 2 =0  Test Statistic 7STA 291 Summer 2010 Lecture 19

 Government agencies have undertaken surveys of Americans 15 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 121 yes responses out of 306 surveyed while the survey 10 years ago resulted in 108 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 5% level of significance. STA 291 Summer 2010 Lecture 198