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Statistics for Business and Economics | 12th Edition | ISBN: 9780321826237 | Authors: James T. McClave, P. George Benson, Terry T Sincich
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Frequency marketing programs by restaurants. To instill

Chapter 7, Problem 134SE

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QUESTION:

Frequency marketing programs by restaurants. 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. More than 80 million people are members of the frequent flier programs of the airline industry (www.frequentflier.com). 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 \(\alpha = .05\). Does it appear that the frequency program would be profitable for the company if adopted nationwide?

Text Transcription:

alpha = .05

Questions & Answers

QUESTION:

Frequency marketing programs by restaurants. 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. More than 80 million people are members of the frequent flier programs of the airline industry (www.frequentflier.com). 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 \(\alpha = .05\). Does it appear that the frequency program would be profitable for the company if adopted nationwide?

Text Transcription:

alpha = .05

ANSWER:

Solution:

Step 1 of 3:

We have the profit change for restaurants.

$2,232.90

$545.47

$3,440.70

$1,809.10

$6,552.70

$4,798.70

$2,965.00

$2,610.70

$3,381.30

$1,591.40

$2,376.20

$2,191.00

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