Question

3. Whole Foods is an all-natural grocery chain that has 50,000-square-foot stores, up from the industry average of 34,000 sq ft. Sales per square foot of supermarkets average just under $400 per square foot, as reported by USA Today. Suppose that sales per square foot in the most recent fiscal year are recorded for a random sample of 10 Whole Foods supermarkets. The data are as follows:

854 858 801 892 849 807 894 863 829 815

a. Find the point estimate for the average sales per square foot for Whole Foods supermarkets. b. Determine a 95% confidence interval estimate for the average sales per square foot for Whole Foods supermarkets. c. Interpret your confidence interval. Do you think that Whole Foods supermarkets sales per square foot are different from the industry average?

Answer 1

A) The average point estimate () = (854 + 858 + 801 + 892 + 849 + 807 + 894 + 863 + 829 + 815)/10 = 846.2

B) Sample standard deviation (s) = Sqrt(((854 - 846.2)^2 + (858 - 846.2)^2 + (801 - 846.2)^2 + (892 - 846.2)^2 + (849 - 846.2)^2 + (807 - 846.2)^2 + (894 - 846.2)^2 + (863 - 846.2)^2 + (829 - 846.2)^2 + (815 - 846.2)^2)/9) = 32.9

At 95% confidence interval the critical value is t^* = 2.262

Tje 95% confidence interval is

+/- t^* * s/sqrt(n)

= 846.2 +/- 2.262 * 32.9/Sqrt(10)

= 846.2 +/- 23.5

= 822.7, 869.7

Wr are 95% confidence that the true average sales per square foot for whole Foods supermarkets lies in the above confidence interval.

As 400 doesn't lie in the interval, so whole foods super markets sales per square foot are different from the industry average.