A Fast Food Chain Test Marketing a New Sandwich Chose $E ( y )$

Essay

A fast food chain test marketing a new sandwich chose 18 of its stores in one major
metropolitan area. Nine of the stores were in malls and nine were free standing. The sandwich was offered at three different introductory prices. The table shows the number of new sandwiches sold at each location for each location type and price combination.

Number of New Sandwiches Sold


a. Write a model for the mean number of sandwiches sold, $E ( y )$ , assuming that the relationship between $E ( y )$ and price, $x _ { 1 }$ , is first-order.
b. Fit the model to the data.
c. Write the prediction equations for mall and free-standing stores.
d. Do the data provide sufficient evidence that the change in number of sandwiches sold with respect to price is different for mall and free-standing stores? Use $\alpha = .01$ .