## [answered] MATH215 Statistical Concepts Names_________________________

Would like to get answers with explanations to the following Hypothesis Testing Worksheet.

Please show any calculator functions and/or Excel formulas used.?

Thanks, David

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

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