The Chief Operating Officer (COO) of a company would like to ensure that employee performance reviews, performed by unit heads, are done as quickly and efficiently as possible. She decides to compare two strategies. In the first strategy, she allocates time during the day (for a period of 1 month) for some of her unit heads to complete performance reviews. In the second strategy, she provides additional pay for after hour time (for 1 month) for some unit heads to complete performance reviews. You may assume that all unit heads review the same number of performance files. A randomly selected sample of 25 unit heads are assigned the first strategy (allocated day time) and the remaining 15 unit heads are assigned to the second strategy (additional pay for after-hour work). For each unit head, the total time (in hours) to complete the performance reviews for the unit is recorded. The sample mean and sample standard deviation for the 25 unit heads in strategy 1 are, respectively, 31.1 hours and 4.5 hours. On the other hand, the sample mean and sample standard deviation for the 15 unit heads in strategy 2 are, respectively, 33.8 hours and 4.2 hours.

[3 marks] Identify the following in this question:

• 1. factors and factor levels
• 1. treatments
• 1. replications

1. [3 marks] Write down an appropriate statistical model to analyze the data in this problem. You must introduce all variables, include all underlying assumptions, and write the interpretation of each parameter within the context of this problem.
2. [5 marks] The COO hypothesizes that, on average, the first strategy results in faster completion of performance review files, and would like to investigate this hypothesis. Formulate proper null and alternative hypotheses and carry out a test of hypothesis to answer test the COO's thought. Provide the details of your calculations.
3. [3 marks] Provide a 95% confidence interval for the difference in the average time spent on performance review files. Compare your conclusion here to that of in part (c). What do you observe? Justify your observation.