Question

Lester Hollar is vice president for human resources for a large manufacturing company. In recent years, he has noticed an increase in absenteeism that he thinks is related to the general health of the employees. Years ago, in an attempt to improve the situation, he began a fitness program in which employees exercise during their lunch hour. To evaluate the program, he selected a random sample of eight participants and found the number of days each was absent in the six months before the exercise program began and in the last six months. Below are the results. Use a 0.05 significance level and determine if it is reasonable to conclude that the number of absences has decline? Use this information to solve the following questions.

A. What is the null hypothesis statement for this problem?

B. What is the alternative hypothesis statement for this problem?

C. What is alpha for this analysis?

D. What is the most appropriate test for this problem? (choose one of the following)

a. t-Test: Paired Two Sample for Means

b. t-Test: Two-Sampled Assuming Equal Variances

c. t-Test: Two-Sample Assuming Unequal Variances

d. z-Test: Two Sample for Means

E. What is the value of the test statistic for the most appropriate analysis?

F. What is the lower bound value of the critical statistic? If one does not exist (i.e. is not applicable for this type analysis), document N/A as your response.

G. What is the upper bound value of the critical statistic? If one does not exist (i.e. is not applicable for this type analysis), document N/A as your response.

H. Is it reasonable to conclude that the number of absences has decline? (choose one of the following)

a. Yes

b. No

I. What is the p-value for this analysis? (Hint: Use this value to double check your conclusion)

Employee	Before	After
1	6	5
2	6	2
3	7	1
4	7	3
5	4	3
6	3	6
7	5	3
8	6	7

Show all work with the right formulas

Answer 1

Number	Before	After	Difference
	6	5	1	0.5625
	6	2	4	5.0625
	7	1	6	18.0625
	7	3	4	5.0625
	4	3	1	0.5625
	3	6	-3	22.5625
	5	3	2	0.0625
	6	7	-1	7.5625
Total	44	30	14	59.5

To Test :-

H0 :-  

H1 :-  

C. What is alpha for this analysis?

level of significance

D. What is the most appropriate test for this problem?

t-Test: Paired Two Sample for Means

E. What is the value of the test statistic for the most appropriate analysis?

Test Statistic :-





t = 1.6977

Test Criteria :-
Reject null hypothesis if


Result :- Fail to reject null hypothesis

F. What is the lower bound value of the critical statistic?

Lower bound critical value = -1.895

G. What is the upper bound value of the critical statistic?

Since the test is left sided, hence there is no upper bound of the critical statistic.

H. Is it reasonable to conclude that the number of absences has decline?

Conclusion :- Accept null hypothesis ( H0 )

There is no sufficient evidence to support the claim that the number of absences has decline.

I. What is the p-value for this analysis

P ( t > 1.6977 ) = 0.0667