# case analysis 109

You manage Human Relations for your company. One of your sales managers has retired, leaving an opening. You are considering two different employees for the position. Both are highly qualified so you have decided to evaluate their sales performance for the past year.

**Use** the Week 4 Data Set to **create** and **calculate** the following in Excel^{Â®}:

- You are interested in knowing the average weekly sales for all of the sales reps in your company. You only have a sample of 50. You know you can develop a range in which you might be able to find the average for all of the reps. Determine the upper and lower limits of this range as follows:
- Calculate the range in which you would expect to find the average weekly sales 90% of the time?
- Calculate the impact of increasing the confidence level to 95%?
- Calculate the impact of increasing the sample size to 150, assuming the same mean and standard deviation, but allowing the confidence level to remain at 90%?

- Based on the calculated confidence interval for weekly sales on the sample of 50 reps at a 90% confidence level:
- Calculate both Reps’ average weekly performance and highlight if it is greater than the population mean.

- You want to determine whether there is a statistically different average weekly sales between Sales Rep A and Sales Rep B.
- Create Null and Alternative Hypothesis statements that would allow you to determine whether their sales performance is statistically different or not.
- Use a significance level of .05 to conduct a z-test of two sample means using the Excel Data Analysis Toolpak to compare the average weekly sales of the two candidates.
- Calculate the p-value.
- Who will you recommend for promotion and why?

- Regarding your choice for promotion:
- Determine whether this person’s average weekly sales are greater than the average weekly sales for the 50 sales reps whose data you used to develop confidence intervals.
- Create Null and Alternative Hypothesis statements that would allow you to determine whether the new Sales Manager’s weekly average sales are greater than the sample of Sales Reps.
- Use a significance level of .05 to conduct a z-test of two sample means using the Excel Data Analysis Toolpak to compare the average weekly sales of both.
- Calculate the p-value?
- How has this new analysis impacted on your decision?