MATH215 Statistical Concepts Names_______________________________ Two Sample Hypothesis Test Worksheet Part I: First identify if the samples here are dependent (paired) or independent. Then properly state the null and alternative hypotheses for the following situations: 1. Compare the heights of husbands to the heights of their wives. Twenty couples were chosen and their heights measured. Test the hypothesis that the mean of the differences is equal to zero. 2. In a clinical trial for the side effects of a drug, test the hypothesis that the proportion of subjects who experienced the side effects when given the drug is greater than the proportion of subjects who experienced the side effects when given a placebo. 3. Test the hypothesis that employees with a high school diploma have lower mean annual income than employees with a bachelor's degree. 4. A health program measured the weights of a sample of women before and after a one month long exercise program. Test that the mean of the differences between before and after weights is different from zero. Part II: 1. The National Endowment for the Humanities sponsors summer institutes to improve the skills of high school teachers of foreign languages. One such institute designed a summer program for French language teachers and they wanted to test the success of the program before they implemented it in their permanent summer schedules. To determine the success of the program, they randomly divided 40 French teachers into two groups of 20. One group completed the new program in 4 weeks and the second group completed the existing old program during this time. At the end of the 4 weeks, the teachers in both programs were given the listening test of Modern Language Association for the understanding of spoken French. The test results are given in the following table. The maximum possible score on the test is 36. 1 030914 MATH215 Statistical Concepts Names_______________________________ Scores of the teachers from old program 19 28 31 24 23 28 32 30 25 19 20 25 23 32 30 29 27 21 24 24 Scores of the teachers from new program 27 26 25 19 22 35 19 27 31 34 28 28 19 36 23 27 33 32 29 26 a. Are these dependent or independent samples? Explain your answer. b. Find the mean test scores program) and x N x O = ___________ x N (the mean score of teachers who completed the new (the mean score of teachers who completed the old program). x O = ___________ c. Find the standard deviations of both data sets. sN = ___________ s O = ___________ d. With 95% confidence, determine the difference between the two mean scores. Interpret the meaning of this confidence interval for the success of the program. 2 030914 MATH215 Statistical Concepts Names_______________________________ e. Test the hypothesis that the new program is successful to improve the language skills of French language teachers at 0.05 level of significance. Show all five steps of the hypothesis testing process including the interpretation. (Assume that all the scores from such tests are normally distributed. Calculator menu may be used. Points will be deducted for missing steps.) 2. The following summer, the institute wanted to test the success of this new program in a different way. They enrolled 20 French language teachers in the 4-week program. At the beginning of this period, the teachers were given the listening test of Modern Language Association for the understanding of spoken French. After they completed the program in 4 weeks, the listening test was given again. (The actual French spoken in the two tests was different, so that simply taking the first test should not improve the score on the second test.) Each teacher's pre-test and post-test results are listed in the following table. The maximum possible score on the test is 36. Teacher 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Pre-test score 32 31 29 10 30 33 22 25 32 20 30 20 24 24 31 30 15 32 23 23 Post-test score 34 31 35 16 33 36 24 28 26 26 36 26 27 24 32 31 15 34 26 26 3 030914 MATH215 Statistical Concepts Names_______________________________ a. Are these dependent or independent samples? Explain your answer. b. Add another column to the table above for the difference between the pre-test and post-test scores. Find that difference for each teacher. c. Find the mean and the standard deviation of the difference column. x D = _______________ s = ____________________ D d. Test the hypothesis that the new program is successful to improve the language skills of French language teachers at a 0.05 level of significance. Show all five steps of the hypothesis testing process including the interpretation. (Assume that all the scores from such tests will be normally distributed. Use of the calculator menu is fine. Points will be deducted for missing steps.) 3. How are the results from the two tests in the previous parts different? Why is that? Which test do you think would produce more reliable results in this case? Explain your reason. 4 030914