Question

Lester Hollar is vice president for human resources for a large manufacturing company. In recent years, he has noticed an increase in absenteeism, which he thinks is related to the general health of the employees. Four 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.

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

At the .05 significance level, can he conclude that the number of absences has declined? Estimate the p-value.

a. State the decision rule for 0.05 significance level: H₀ : μ_d≤ 0; H₁ : μ_d > 0. (Round the final answer to 3 decimal places.)

Reject H₀ if t >  .

b. Compute the value of the test statistic. (Round the final answer to 3 decimal places.)

Value of the test statistic            

c. Estimate the p-value? (Round the final answer to 4 decimal places.)

d. What is your decision regarding H₀?

At the 0.05 significance level,  (Click to select)  reject  do not reject  H₀.

Answer 1

First we perform the hypothesis testing:

a. State the decision rule for 0.05 significance level:

H₀ : μ_d  ≤ 0;

H₁ : μ_d > 0.

Reject H₀ if t >1.895.  .

b. Compute the value of the test statistic. (Round the final answer to 3 decimal places.)

Value of the test statistic :1.106   

c. Estimate the p-value? (Round the final answer to 4 decimal places.)

0.1526

d. What is your decision regarding H₀?

Do not reject Ho since calculated test statistic is less than tabulated t-statistics and p-value is greater than 0.05.