Lester Hollar is vice president for human resources for a large manufacturing co

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 last six months. Below are the results. Employee 1 2 3 4 5 6 7 8                Before 7 7 5 6 4 5 7 7                    After 5 2 1 2 3 6 3 7

  Click here for the Excel Data File At the 0.05 significance level, can he conclude that the number of absences has declined? Hint: For the calculations, assume the "Before" data as the first sample. Reject H0 if t > . (Round your answer to 3 decimal places.) The test statistic is . (Round your answer to 3 decimal places.) The p-value is . Decision: H0.

Explanation / Answer

The statistical software output for this paired t test is:

Paired T hypothesis test:
D = 1 - 2 : Mean of the difference between Before and After
H0 : D = 0
HA : D > 0
Hypothesis test results:

Also,

For a right tailed test with 7 degrees of freedom and 0.05 level of significance,

Ctitical t value = 1.895

Hence,

Reject Ho is t > 1.895

Test statistic = 3.054 [T - Stat in the summary output]

p - value = 0.0092 [p - value in the summary output]

Since p - value is less than 0.05, reject Ho.

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