Julia Jackson operates a franchised restaurant that specializes in soft ice cream cones and sundaes. Recently she received a letter from corporate headquarters warning her that her shop is in danger of losing its franchise because the average sales per customer have dropped “substantially below the average for the rest of the corporation.” The statement may be true, but Julia is convinced that such a statement is completely invalid to justify threatening a closing. The variation in sales at her restaurant is bound to be larger than most, primarily because she serves more children, elderly, and single adults rather than large families who run up big bills at the other restaurants. Therefore, her average ticket is likely to be smaller and exhibit greater variability. To prove her point, Julia obtained the sales records from the whole company and found that the standard deviation was $2.45 per sales ticket. She then conducted a study of the last 71 sales tickets at her store and found a standard deviation of $2.95 per ticket. Is the variability in sales at Julia’s franchise, at the 0.05 level of significance, greater than the variability for the company?
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