Hypothetical sales
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. The data showing a sample of their respective sales performance is in the Excel worksheet.
1. Annual sales data is provided for a sample of 50 employees.
- Determine the range of values in which you would expect to find the average weekly sales for the entire sales force in your company 90% of the time
- What is the impact of increasing the confidence level to 95%?*
- What is 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%?*
2. 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.
- Based on your hypothesis statements, provide an example of a Type I and a Type II error, respectively.
- Using a significance level of .05, conduct a t-test of independent samples when the standard deviation of the population is unknown to compare the average weekly sales of the two candidates. (NOTE: YOU CAN DO THIS VERY QUICKLY IN EXCEL USING THE DATA ANALYSIS TOOLPAK!)
- What is the p-value?
- Based on the p-value, is there a statistically significant difference between the two reps being considered for the manager’s position? Explain your reasoning.
- Who would you recommend to be promoted to Sales Manager – Rep A or Rep B? Why?
All Sales Representatives are expected to meet an average weekly sales quota of $4500.
- Create Null and Alternative Hypothesis statements that would allow you to determine whether the weekly sales of the individual you have decided to promote in #4 (Rep A or Rep B) exceeds the company quota.
- Based on your hypothesis statements, provide an example of a Type I and a Type II error, respectively.
- Using a significance level of .05, conduct a one sample mean hypothesis test to determine whether the performance of your chosen candidate exceeds the quota by a statistically significant amount?
- What is the p-value?
- Based on the p-value, what is your conclusion?
| SAMPLE – WEEKLY SALES | SAMPLE OF WEEKLY SALES FOR REP A AND B | |||||
| # Sales Rep | Weekly Sales $ | Week # | Weekly Sales – A | Weekly Sales – B | ||
| 1 | 1228 | 1 | 4657 | 5839 | ||
| 2 | 7374 | 2 | 6133 | 2602 | ||
| 3 | 1055 | 3 | 3438 | 2830 | ||
| 4 | 1859 | 4 | 7394 | 4763 | ||
| 5 | 3938 | 5 | 4327 | 3740 | ||
| 6 | 1692 | 6 | 2552 | 1315 | ||
| 7 | 569 | 7 | 7063 | 1599 | ||
| 8 | 4059 | 8 | 7844 | 1629 | ||
| 9 | 3689 | 9 | 6898 | 2416 | ||
| 10 | 607 | 10 | 4003 | 2107 | ||
| 11 | 1370 | 11 | 6884 | 4237 | ||
| 12 | 3735 | 12 | 4007 | 6322 | ||
| 13 | 3305 | 13 | 7214 | 2710 | ||
| 14 | 7228 | 14 | 2358 | 5890 | ||
| 15 | 6279 | 15 | 7745 | 5119 | ||
| 16 | 1671 | 16 | 1337 | 5184 | ||
| 17 | 5708 | 17 | 1052 | 3439 | ||
| 18 | 2569 | 18 | 6056 | 4828 | ||
| 19 | 4163 | 19 | 1495 | 3667 | ||
| 20 | 1519 | 20 | 3530 | 2518 | ||
| 21 | 7734 | 21 | 4749 | 6073 | ||
| 22 | 784 | 22 | 3833 | 5566 | ||
| 23 | 6766 | 23 | 7869 | 4555 | ||
| 24 | 7261 | 24 | 4541 | 5867 | ||
| 25 | 5034 | 25 | 6882 | 6039 | ||
| 26 | 7115 | 26 | 3868 | 1032 | ||
| 27 | 6291 | 27 | 5934 | 4834 | ||
| 28 | 6287 | 28 | 4447 | 3687 | ||
| 29 | 2080 | 29 | 5504 | 2214 | ||
| 30 | 7621 | 30 | 5554 | 4659 | ||
| 31 | 1047 | |||||
| 32 | 6517 | |||||
| 33 | 5172 | |||||
| 34 | 3876 | |||||
| 35 | 5429 | |||||
| 36 | 4538 | |||||
| 37 | 3786 | |||||
| 38 | 2510 | |||||
| 39 | 4863 | |||||
| 40 | 7246 | |||||
| 41 | 1175 | |||||
| 42 | 641 | |||||
| 43 | 4269 | |||||
| 44 | 7034 | |||||
| 45 | 3406 | |||||
| 46 | 2256 | |||||
| 47 | 3182 | |||||
| 48 | 5178 | |||||
| 49 | 4428 | |||||
| 50 | 1189 | |||||
