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. A recent survey using a sample of 200 women shoppers in Tampa, Florida, 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 α = .01.
Outlet Percentage
Other 35
Wal-Mart 25
Department Stores 10
Mail Order 15
Kohl's 10
J.C. Penney 5
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? Use α = .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
a. Conduct a test of independence using critical value approach to determine whether employee health insurance coverage is independent of the size of the company. Use α = .005.
b. What is the p- value, and what is your conclusion?
c. 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.
4. FlightStats, Inc., collects data on the number of flights scheduled and the number of flights flown at major airports throughout the United States. FlightStats data showed 56% of flights scheduled at Newark, La Guardia, and Kennedy airports were flown during a three-day snowstorm. All airlines say they always operate within set safety parameters- if conditions are too poor, they don't fly. The following data show a sample of 600 scheduled flights during the snowstorm. Use the chi- square test with a .10 level of significance to determine whether or not flying/ not flying in a snowstorm is independent of Airliner. What is your conclusion based on Critical Value test? Is it any different from conclusion based on a p-value approach?
Flight American Continental Delta United
Yes 70 105 95 45
No 80 55 85 65
5. The number of incoming phone calls defined by a Random Variable X at a company switchboard during 1- minute intervals is believed to have a Poisson distribution. Use a .05 level of significance and the following data to test the assumption that the incoming phone calls follow a Poisson distribution.
xObserved Freq.
0 14
1 33
2 48
3 44
4 30
5 15
6 9
7 6
8 1