In exercises that call for two-sample procedures, you may use either of the two approximations for the degrees of freedom that we have discussed: the value given by your software or the smaller of and . Be sure to state clearly which approximation you have used.

Question 7.65

7.65 Sales of small appliances.

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 an SRS of 70 stores this month shows mean sales of 53 units of a small appliance, with standard deviation 12 units. During the same month last year, an SRS of 58 stores gave mean sales of 50 units, with standard deviation 10 units. An increase from 50 to 53 is a rise of 6%. The marketing manager is happy, because sales are up 6%.

  1. Use the two-sample procedure to give a 95% confidence interval for the difference in mean number of units sold at all retail stores.
  2. Explain in language that the manager can understand why he cannot be confident that sales rose by 6%, and that in fact sales may even have dropped.

7.65

(a) (−0.91, 6.91). (b) With 95% confidence, the mean change in sales from last year to this year is between −0.91 and 6.91. Because the interval covers 0 and includes some negative values, it is possible sales have actually decreased.