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. 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 six months following the exercise program. Below are the results.

Employee	Before	After
Bauman	6	3
Briggs	5	2
Dottellis	5	1
Lee	7	2
Perralt	4	2
Rielly	5	6
Steinmetz	7	3
Stoltz	6	7

At the 0.010 significance level, can he conclude that the number of absences has declined? Estimate the p-value.

1. State the decision rule for 0.010 significance level. (Round your answer to 3 decimal places.)

2. Compute the test statistic. (Round your answer to 3 decimal places.)

3. The p-value is

• Between 0.01 and 0.025

• Between 0.001 and 0.005

• Between 0.005 and 0.01

4. State your decision about the null hypothesis.

• Do not reject H₀

• Reject H₀

Answer 1

Solution:

Given:

Significance level = 0.010

We have to test if  the number of absences has declined.

Part a) State the decision rule for 0.010 significance level.

n = Number of pairs of observations = 8

df = n - 1 = 8 - 1 = 7

One tail area = left tail area = 0.01

Find t critical value:

t critical value = -2.998

This is negative , since this is left tailed test.

Thus  the decision rule is :

Reject the null hypothesis H0, if t test statistic - 2.998

( Note: Answer depends on how we take differences between before and after,  if we take difference = After - Before, then this is left tailed test, and hence answer is negative, if we take difference = Before - After, then answer would be positive and right tailed test.)

Part b) Compute the test statistic.

where

Employee	Before	After	di	di^2
Bauman	6	3	-3	9
Briggs	5	2	-3	9
Dottellis	5	1	-4	16
Lee	7	2	-5	25
Perralt	4	2	-2	4
Rielly	5	6	1	1
Steinmetz	7	3	-4	16
Stoltz	6	7	1	1

Thus

and

thus

Part c) The p-value is:

df = n - 1= 8 - 1 = 7

Look in t table for df = 7 row and find an interval in which t = 2.967 fall, then find corresponding one tail area interval.

t = 2.967 fall between 2.365 and 2.998

corresponding one tail is between 0.01 and 0.025

thus 0.01 < p-value < 0.025

The p-value is:

Between 0.01 and 0.025

Part d) State your decision about the null hypothesis.

Since p-value is Between 0.01 and 0.025, that is, p-value > 0.01 significance level , we fail to reject null hypothesis H0.

Thus we get:

Do not reject H_0.