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Descriptive Statistics and Hypothesis Test

Kimble Products: Is There a Difference in the Commissions?

At the January national sales meeting, the CEO of Kimble Products was questioned extensively regarding the company policy for paying commissions to its sales representatives. The company sells sporting goods to two major markets. There are 40 sales representatives who call directly on large volume customers, such as the athletic departments at major colleges and universities and professional sports franchises. There are 30 sales representatives who represent the company to retail stores located in shopping malls and large discounters such as Kmart and Target.

Upon his return to corporate headquarters, the CEO asked the sales manager for a report comparing the commissions earned last year by the two parts of the sales team. The information is reported below.

Would you conclude that there is a difference? Be sure to include in the report a graphical description and appropriate descriptive statistics of the two groups.

Commissions Earned by Sales Representatives Calling on Athletic Departments ($)
354 87 1676 1187 69 3202 680 39 1683 1106
883 3140 299 2197 175 159 1105 434 615 149
1168 278 579 7 357 252 1602 2321 4 392
416 427 1738 526 13 1604 249 557 635 527

Commissions Earned by Sales Representatives Calling on Large Retailers ($)
1116 681 1294 12 754 1206 1448 870 944 1255
1213 1291 719 934 1313 1083 899 850 886 1556
886 1315 1858 1262 1338 1066 807 1244 758 918

Solution Preview

We're going to use a two-sample, two-sided t-test to compare the means of the two groups. (In your paper, include summary statistics of the data first - mean, median, etc. - I've included that information below.)

Our null statistic is that the means of the two groups are equal, and our alternative hypothesis is that the means of the two groups are different.

The test statistic is:

where x-bar and y-bar are the sample means, Sx and Sy are the sample standard deviations, and n1 and n2 are the sample sizes.

For the first group (athletic departments), the mean is 822.275, the standard deviation is 829.853, and n = 40.

For the second group (large retailers), the mean is 1059.2, the standard deviation is 338.971, and n = 30.

You can use those numbers to do the t-test by hand, but ...

Solution Summary

The solution includes a description of the data sets (mean, standard deviation, five-number summary, median, histogram, etc.) and a t-test to determine if the means of the two groups are significantly different.

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