Question

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. A random sample of 36

stores this year shows mean sales of 52
units of a small appliance with a standard deviation of 5
units. During the same point in time last year, a random sample of 49
stores had mean sales of 46
units with standard deviation 14
units.

It is of interest to construct a 95 percent confidence interval for the difference in population means 1−2
, where 1
is the mean of this year's sales and 2
is the mean of last year's sales.

Enter values below rounded to three decimal places.

(a) The estimate is:
.

(b) The standard error is:
.

Answer 1

Explanation:

(a) The estimate for the difference in population means is 6.000.

(b) The standard error for the difference in population means is 3.208.

Conclusion:

Based on the given data, the 95% confidence interval for the difference in population means between this year's sales and last year's sales is between -0.608 and 12.608. This suggests that the population mean for this year's sales is likely to be higher than the population mean for last year's sales. This is supported by the fact that the estimate for the difference in population means is 6.000, which is greater than 0.