HW 7 ANOVA

HW

7

ANOVA

Due Date Wednesday

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1

1/

2

1/2012.

NO LATE HW WILL BE ACCEPTED

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 1

8

credit card purchases revealed the following (see table)

$61

$42

$56

$56

$72

Purchase	Visa	American Express	Macy’s Credit Card
1		$ 6 1	$8 5
2	$28			$56	$25
3		$ 4 2	$44
4	$33		$72	$31
5	$51	$ 9 8	$29
6
7
8
9

Purchases were rounded to the nearest dollar.

Questions:

1. Can you use the t-test to answer the above research question? (5 points.)

2. Assume the answer to the above question is YES. Indicate how many hypothesis tests are you going to conduct? (20 points.)

3. Assume the answer to the above question is NO. Indicate why you cannot use the t-test to answer the above research question? (25 points.)

4. What test statistic are you going to test the above research question? (10 points.)

5. Compare and contrast the test statistic (from question 4) to the t test statistic? (50 points.)

6. Identify and list the types of variables in the above problem? (20 points.)

7. Write the null hypothesis in words and symbols (10 points.)

8. Write the alternative hypothesis in words and symbols (10 points.)

9. Compute the test statistic for the above hypothesis (100 points)

10. At alpha equal to 0.05, determine the critical value for the above test (30 points.)

11. What is your decision regarding the above research question and indicate why? (50 points)

Question 2: A1 limousine service offers service to and from Newark airport to Princeton New Jersey. John Wheels, the president of A1 limo, is considering two routes to Princeton. One route via US 1 and the other is via the NJ Turnpike. He is interested in the amount of time it takes to drive to the airport using each route and then compare the results. He instructed his drivers to drive using both routes and record the time (in minutes) it takes the drivers to arrive at Princeton. The table below shows the travel time

Route US 1

NJ Turnpike

100

90

95

100

120

95

75

90

Using the 0.05 significance level, is there a difference in the variation in the driving times for the two routes? ( 120 points.)