Question

1. The personnel manager of a large manufacturing plant (1,000+ employees) suspects a difference in the mean amount of sick leave taken by workers on the day shift compared to the night shift. A random sample of 38 day workers had a mean of 10.6 days sick leave last year with a standard deviation of 3.3 days. A random sample of 41 night workers had a mean of 12.9 days sick leave last year with a standard deviation of 4.5 days. Assume that sick days are distributed normally for both the night and day shifts. Use an α = 5% level of significance to test the claim that there is a difference in the mean amount of sick leave taken by workers on the day shift compared to the night shift.

1. State the null and alternative hypotheses [3]

2. Check the assumptions [4]

3. Give the test statistic [2]

4. Give the P-value and the conclusion reached about the null hypothesis based on the P-value [2]

5. Summarize the final conclusion in the context of the claim [2]

6. For this problem what type of error did you potentially commit based on your answer in (d)? [2]

7. Construct a 95% confidence interval for the mean difference in sick days between day and night shift workers. [3]

8. Interpret the interval in (g) [3]

1. Based on your interval, which workers take more days off? [2]

Answer 1