The Human Resources (HR) Director would like to implement a three-week training

Question

The Human Resources (HR) Director would like to implement a three-week training program for the manufacturing department employees, which she believes would improve their productivity. In order to have supporting data to support her belief, with the approval of the VP Operations, the three-week training program is given to 15 employees chosen randomly from the manufacturing department. We observed the number of items produced by these 15 employees before and after their training. The observation period before and after the training was 20 working days long.

You have been tasked to conduct the study to validate the HR Director`s belief. Use a level of significance of 1%.

a. Using Minitab, do the appropriate hypotheses test for this study.

i. Report your finding to the HR Director by writing a one-paragraph report.

ii. Are the two data sets independent or not? Explain your answer.

b. Now show the manual calculations for the test in (a). You can use the Minitab descriptive statistics report to obtain the summaries to allow you to do the calculation.

i. Do you come to the same conclusion that you did in (a)?

c. Calculate manually the 99% confidence interval. What are your findings? Do you come to the same conclusion that you did in (a)?

Employee Before After 1 15 17 2 13 16 3 8 10 4 9 9 5 7 9 6 12 13 7 11 14 8 12 15 9 11 14 10 9 11 11 10 14 12 12 11 13 11 13 14 7 10 15 12 13

Explanation / Answer

We have to conduct 2 sample t test to compare the productivity. As population variance is unknown and sample size(15)<30, we should opt for 2 sample t instead of z test.

Employee Before After 1 15 17 2 13 16 3 8 10 4 9 9 5 7 9 6 12 13 7 11 14 8 12 15 9 11 14 10 9 11 11 10 14 12 12 11 13 11 13 14 7 10 15 12 13 Sum 159 189 Average 10.6 12.6 variance 5.114286 6.257143 sd 2.261479 2.501428 t statistics -2.29704 (B18-C18)/SQRT((B19+C19)/15) df 28 15+15-2

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