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 in the sample had the changes in profit in the data file. Note that if number is negative, it represents a decrease in profits. a. compute the mean and standard deviation of the changes in profit for these 12 restaurants b. Find a 99% confidence interval for the average changes in profit c. The restaurants not in the sample had an average increase in profits of $1,000 over the same 3 months. Conduct a hypothesis test to determine whether the mean profit change for restaurants with frequency programs was significantly bigger from (in a statistical sense) $1,000. Report the P-value and test at alpha=0.01 level.

Profit 2232.9 6552.7 3381.3 545.47 4798.7 1591.4 3440.7 2965 2376.2 1809.1 2610.7 -2191