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 in to 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.

Scores of the teachers from old program

Scores of the teachers from new program

19

27

28

26

31

25

24

19

23

22

28

35

32

19

30

27

25

31

19

34

20

28

25

28

23

19

32

36

30

23

29

27

27

33

21

32

24

29

24

26

a.Are these dependent or independent samples?Explain your answer.

b.Find the mean test scores (the mean score of teachers who completed the new program) and(the mean score of teachers who completed the old program).

= ___________= ___________

c.Find the standard deviations of both data sets.

= ___________= ___________

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.

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-weeks 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

Pre-test score

Post-test score

1

32

34

2

31

31

3

29

35

4

10

16

5

30

33

6

33

36

7

22

24

8

25

28

9

32

26

10

20

26

11

30

36

12

20

26

13

24

27

14

24

24

15

31

32

16

30

31

17

15

15

18

32

34

19

23

26

20

23

26

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.

= _______________ s_D = ____________________

d.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 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.