# MATH215 Statistical Concepts Names

MATH215 Statistical Concepts Names_______________________________ Two Sample Hypothesis Test WorksheetPart I:First identify if the samples here are dependent (paired) or independent. Then properly state the nulland alternative hypotheses for the following situations: 1. Compare the heights of husbands to the heights of their wives. Twenty couples were chosen andtheir 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 subjectswho experienced the side effects when given the drug is greater than the proportion of subjectswho experienced the side effects when given a placebo.3. Test the hypothesis that employees with a high school diploma have lower mean annual incomethan employees with a bachelor’s degree. 4. A health program measured the weights of a sample of women before and after a one monthlong exercise program. Test that the mean of the differences between before and after weightsis different from zero. Part II: 1. The National Endowment for the Humanities sponsors summer institutes to improve theskills of high school teachers of foreign languages. One such institute designed a summerprogram for French language teachers and they wanted to test the success of the programbefore they implemented it in their permanent summer schedules. To determine thesuccess 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 theexisting old program during this time. At the end of the 4 weeks, the teachers in bothprograms were given the listening test of Modern Language Association for theunderstanding of spoken French. The test results are given in the following table. Themaximum possible score on the test is 36. 1030914 MATH215 Statistical Concepts Names_______________________________ Scores of theteachers from oldprogram1928312423283230251920252332302927212424 Scores of theteachers from newprogram2726251922351927313428281936232733322926 a. Are these dependent or independent samples? Explain your answer. b. Find the mean test scoresprogram) 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. Interpretthe meaning of this confidence interval for the success of the program. 2030914 MATH215 Statistical Concepts Names_______________________________ e. Test the hypothesis that the new program is successful to improve the language skills ofFrench language teachers at 0.05 level of significance. Show all five steps of the hypothesistesting process including the interpretation. (Assume that all the scores from such tests arenormally distributed. Calculator menu may be used. Points will be deducted for missingsteps.) 2. The following summer, the institute wanted to test the success of this new program in adifferent way. They enrolled 20 French language teachers in the 4-week program. At thebeginning of this period, the teachers were given the listening test of Modern LanguageAssociation for the understanding of spoken French. After they completed the program in 4weeks, the listening test was given again. (The actual French spoken in the two tests wasdifferent, so that simply taking the first test should not improve the score on the secondtest.) Each teacher’s pre-test and post-test results are listed in the following table. Themaximum possible score on the test is 36. Teacher1234567891011121314151617181920 Pre-test score3231291030332225322030202424313015322323 Post-test score3431351633362428262636262724323115342626 3030914 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 andpost-test scores. Find that difference for each teacher.c. Find the mean and the standard deviation of the difference column. ´x D = _______________ s = ____________________Dd. Test the hypothesis that the new program is successful to improve the language skills ofFrench language teachers at a 0.05 level of significance. Show all five steps of thehypothesis testing process including the interpretation. (Assume that all the scores fromsuch tests will be normally distributed. Use of the calculator menu is fine. Points will bededucted for missing steps.) 3. How are the results from the two tests in the previous parts different? Why is that? Whichtest do you think would produce more reliable results in this case? Explain your reason. 4030914