To instill customer loyalty, airlines, hotels, rental car companies, and credit card companies (among others) have initiated frequency marketing programs that reward their regular customers. A large fast-food restaurant chain wished to explore the profitability of such a program. They randomly selected 12 of their 1,200 restaurants nationwide and instituted a frequency program that rewarded customers with a $5.00 gift certificate after every 10 meals purchased at full price. They ran the trial program for 3 months. The restaurants not in the sample had an average increase in profits of $1,050 over the previous 3 months, whereas the restaurants in the sample had the following changes in profit.

Note that the last number is negative, representing a decrease in profits.
a. Specify the appropriate null and alternative hypotheses for determining whether the mean profit change for restaurants with frequency programs was significantly greater (in a statistical sense) than $1,050.
b. Conduct the test of part b using α = .05. Does it appear that the frequency program would be profitable for the company if adopted nationwide?

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$3,440.70 $2,965.00 $2,376.20 $ 545.47 $1,809.10 $6,552.70 $2,610.70 $4,798.70 $1,591.40 $3,381.30 -$2,191.00