University of South Florida Shopper Database Business Worksheet

HW Problems:

 

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, 30mail 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.

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 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. State the Hypotheses and the conclusion. Use α = .005.

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

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. State the Hypotheses. What is your conclusion based on Critical-Value test? Is it any different from conclusion based on a p-value approach? Sample data follows:

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. State the Hypotheses as well as the conclusion.

x

Observed Freq.

0

14

1

33

2

48

3

44

4

30

5

15

6

9

7

6

8

1

6.A salesperson makes four calls per day. A sample of 100 days gives the following frequencies of sales volumes.

Number of Sales

Observed Frequency (Days)

0

30

1

40

2

20

3

8

4

2

Records show sales are made to 30% of all sales calls. Assuming independent sales calls, the number of sales per day should follow a binomial distribution. Assume that the population has a binomial distribution with n = 4, p =.25, and x = 0, 1, 2, 3, and 4.

a.Compute the expected frequencies for x = 0, 1, 2, 3, and 4 by using the binomial probability function. Combine categories if necessary to satisfy the requirement that the expected frequency is five or more for all categories.

b.Use the goodness of fit test to determine whether the assumption of a binomial distribution should be rejected. State the Hypotheses and the conclusion. Use α = .10. Note: Because no parameters of the binomial distribution were estimated from the sample data, the degrees of freedom are k-1 where k is the number of categories.

7.A lending institution supplied the following data on loan approvals by four loan officers. Conduct an appropriate Hypothesis test to determine whether the loan approval decision is independent of the loan officer reviewing the loan application.

 

Loan Approval Decision

 

Loan Officer

Rejected

Approved

Total

Sean

14

12

26

Bruce

14

18

32

Debbie

16

34

50

Susie

16

26

42

Total

60

90

150

  • State the Null and Alternate Hypotheses.
  • Determine the value of the test statistic. Show all the steps in your solution.
  • Determine p-value. Conduct Hypothesis test using p-value approach with α = .025. What is the test decision?
  • Determine Critical-Value. Conduct Hypothesis test using Critical-Value approach with α = .05. What is the test decision?
  • Do the results in parts c) and d) lead to different conclusions? Why or Why not?
  • Based on test decisions under parts c) and d), what conclusion would you draw?

 

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