Macy's Department stores accepts several credit cards. The chief operating officer of Macy's is interested in finding out whether Macy's customers use Macy's credit card more often than some other credit cards like Visa and American Express. The CEO is interested in finding out of there is a difference in the mean amounts (dollars) charged by customers on their Visa, American Express, and Macy's Dept. Store credit card. A random sample of 18 credit card purchases revealed the following (see table)
|
Purchase
|
Visa
|
American Express
|
Macy's Credit Card
|
|
1
|
$61
|
$85
|
$61
|
|
2
|
$28
|
$56
|
$25
|
|
3
|
$42
|
$44
|
$42
|
|
4
|
$33
|
$72
|
$31
|
|
5
|
$51
|
$98
|
$29
|
|
6
|
$56
|
$56
|
|
|
7
|
|
$72
|
|
|
8
|
|
|
|
|
9
|
|
|
|
Questions:
- Can you use the t-test to answer the above research question?
- Assume the answer to the above question is YES. Indicate how many hypothesis tests are you going to conduct?
- Assume the answer to the above question is NO. Indicate why you cannot use the t-test to answer the above research question?
- What test statistic are you going to test the above research question?
- Compare and contrast the test statistic (from question 4) to the t test statistic?
- Identify and list the types of variables in the above problem?
- Write the null hypothesis in words and symbols
- Write the alternative hypothesis in words and symbols
- Compute the test statistic for the above hypothesis
- At alpha equal to 0.05, determine the critical value for the above test
- What is your decision regarding the above research question and indicate why?