The effect of store layout on sales is of strong interest to retailers. In an experiment involving the layout of nonfood sections of supermarkets in the United Kingdom, researchers compared the impact of switching to alternative layouts— including the boutique layout and the free flow layout— for a number of similar sized, randomly selected supermarkets that had been using the standard grid (parallel aisles) layout (source: The Location and Merchandising of non food in Supermarkets, C. Hart, M. Davies, utdt.edu). Assume that the data below shows the change in sales per square foot (converted to US$) for six stores that switched to the boutique layout in their nonfood sections and six stores that switched to the free flow layout.

a. Compute the sample means and sample standard deviations (s₁ and s₂) here. 

b. Compute the pooled estimate of population standard deviation. 

c. Using the pooled estimate in part b, construct and interpret the 95% confidence interval estimate of the difference between the average change in sales for all similar sized stores that would switch to the boutique layout and the average change in sales for all similar sized stores that would switch to the free flow layout. Be sure to use the appropriate t-score for your interval. For the two populations represented, assume that the sales per square foot values are normally distributed, with equal standard deviations.

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Sales Change/ sq. ft. $9 Sales Free-Flow Layout Store M Store N Store O Store P Store Q Store R sq. ft. $4 Layout Store A Store B Store C Store D Store E Store F