Data from the U.S. Shopper Database provided

Subject: Mathematics    / Statistics
Question

1-Data from the U.S. Shopper Database provided the following percentages for women shopping at each of the various outlets. The other category included outlets such as Target, Kmart, and Sears as well as numerous smaller specialty outlets. No individual outlet in this group accounted for more than 5% of the women shoppers.

Outlet

Percentage

Other

35

Wal-Mart

25

Department Stores

10

Mail Order

15

Kohl’s

10

J.C. Penney

5

A recent survey using a sample of 200 women shoppers in Tampa, FL found 60 Wal-Mart, 29 traditional department store, 11 JC Penney, 14 Kohl’s, 30 mail order, and 56 other outlet shoppers. Does this sample suggest that women shoppers in Tampa differ from the preferences expressed in the U.S. Shopper Data-base? What is your conclusion based on both the p-value and critical-value approaches? Use ? = .01.

2-The Wall Street Journal’s Shareholder Scoreboard tracks the performance of 1000 largest U.S. companies. The performance of each company is rated based on the annual total return, including stock price changes and the re-investment of dividends. Ratings are assigned by dividing all 1000 largest U.S. companies into four groups of equal size Group A (top rating), B (second best rating), C (third best rating), and D (bottom most rating). Shown here are the one- year ratings for a sample of 50 largest U.S. companies. Does the sample data provide evidence that the ratings are equally likely for the largest U.S. companies based on both the p-value and critical-value approaches? Use ? = .025.

A

B

C

D

22

9

14

5

3- With double- digit annual percentage increases in the cost of health insurance, more and more workers are likely to lack health insurance coverage. The following sample data provide a comparison of workers with and without health insurance coverage for small, medium, and large companies. For the purposes of this study, small companies are companies that have fewer than 100 employees. Medium companies have 100 to 999 employees, and large companies have 1000 or more employees. Sample data is reported as follows:

Health Insurance

Size of Company

Yes

No

Total

Small

50

25

75

Medium

80

20

100

Large

115

10

125

Total

245

55

300

Conduct a test of independence using critical-value approach to determine whether employee health insurance coverage is independent of the size of the company. State the Hypotheses and the conclusion. Use ? = .005.

What is the p-value? What is your conclusion based on p-value approach?

The USA Today article indicated employees of small companies are more likely to lack health insurance coverage. Use percentages based on the preceding data to support this conclusion.