The Human Resources (HR) Director is implementing a three-week training program for the manufacturing department employees, which she believes will have no impact on their productivity. In order to have data to support her belief, the three-week training program is given to 22 employees chosen randomly from the manufacturing department. We observed the number of items produced by these 22 employees before and after their training. The observation period before and after the training was 22 working days long. You have been tasked to conduct the study to validate the HR Director's belief. Use a level of significance of 5%.

a. Use software for the appropriate parametric hypotheses test for this study.

i. make a brief one paragraph summary to the HR Director .

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

b. Show the manual calculations for the test in part (a). You may use software to obtain the descriptive statistics summaries to do the calculations. i. Do you come to the same conclusion that you did in part (a)?

c. Calculate manually the corresponding 95% confidence interval. What are your results? Is it the same result from part (a)?

d. If you were to use a 99% confidence interval for this study instead. What would your result be? Is it the same result as part (a)? Calculate the confidence interval manually and confirm the calculations using software.

e. Is a parametric or a non-parametric test more appropriate for this study? Draw the corresponding histogram to justify your answer.