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[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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