Question

Sales of a small appliance across months.
A market research firm supplies manufacturers with estimates of the retail sales of their products from samples of retail stores. Marketing managers are prone to look at the estimate and ignore sampling error. Suppose that we have and i.i.d. sample of 60 stores this month and the mean sales of 53 units of a small appliance, with standard deviation (SD) 12 units. During the same month last year, an i.i.d. sample of 58 stores gave mean sales of 50 units, with SD 10 units. An increase from 50 to 53 is a rise of 6%. The marketing manager is happy because sales are up 6%.
(A) Use the two-sample pooled t procedure to give a 95% confidence interval (CI) for the difference in mean number of units sold at all retail stores. In your writeup for this problem, specify the degrees of freedom and the quantile of this critical constant. Use the t -table in the Lecture notes.
(B) Based on the CI you obtained above, what do you conclude about the test of the null hypothesis that there is no difference between the mean number of units sold at the two points in time?
(C) Explain in language that the manager can understand why he cannot be certain that sales rose by 6%, and that in fact sales may even have dropped.

Answer 1

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