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. Using software, conduct the appropriate parametric hypotheses test for this study. i. Report your findings 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 part (a). You can 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 findings? Do you come to the same conclusion that you did in part (a)? d. If you were to use a 99% confidence interval for this study instead. What would your findings be? Do you come to the same conclusion that you did in part (a)? Calculate the confidence interval manually and confirm your 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. Employee 1 Before 15 13 After 17 13 2 3 8 9 4 9 9 5 6 7 12 7 13 12 7 11 13 12 11 9 11 10 11 9 10 11 11 12 11 11 10 12 13 14 15 8 12 13 14 14 16 17 18 9 9 13 12 11 19 11 20 13 12 21 8 9 22 10 10 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. Using software, conduct the appropriate parametric hypotheses test for this study. i. Report your findings 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 part (a). You can 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 findings? Do you come to the same conclusion that you did in part (a)? d. If you were to use a 99% confidence interval for this study instead. What would your findings be? Do you come to the same conclusion that you did in part (a)? Calculate the confidence interval manually and confirm your 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. Employee 1 Before 15 13 After 17 13 2 3 8 9 4 9 9 5 6 7 12 7 13 12 7 11 13 12 11 9 11 10 11 9 10 11 11 12 11 11 10 12 13 14 15 8 12 13 14 14 16 17 18 9 9 13 12 11 19 11 20 13 12 21 8 9 22 10 10
