08 Oct A television documentary on overeating claimed that Americans are about 10 pounds overweight on average (μ).
A television documentary on overeating claimed that Americans are about 10 pounds overweight on average (μ). To test this claim, 18 randomly selected individuals were examined; their average (x?) excess weight was found to be 12.4 pounds, and the sample standard deviation (s) was 2.7 pounds. At a significance level of 0.01, is there any reason to doubt the validity of the claimed 10-pound value?[15 POINTS]
ANSWER:
2. A stockbroker at Critical Securities reported that the mean rate of return on a sample of 10 oil stocks was 12.6 percent with a sample standard deviation of 3.9 percent. The mean rate of return on a sample of 8 utility stocks was 10.9 percent with a sample standard deviation of 3.5 percent. At the .05 significance level, can we conclude that there is more variation in the oil stocks?[15 POINTS]
ANSWER:
3. A study compared the effects of four 1-month point-of-purchase promotions on sales. The unit sales for five stores using all four promotions in different months follow.
Free Sample 78 87 81 89 85
On-pack gift 94 91 87 90 88
Cents off 73 78 69 83 76
Refund by mail 79 83 78 69 81
At the 0.01 level of significance, do the promotions produce different effects on sales? [Note: There are 4 groups to compare, i.e., the 4 marketing methods.][20 POINTS]
ANSWER:
4. William Hawkins, VP of personnel for International Motors, is working on the relationship between a worker’s salary and absentee rate. Hawkins divided the salary range of International into twelve grades or levels (1 being the lowest grade, 12 the highest) and then randomly sampled a group of workers. He determined the salary grade for each worker and the number of days that employee had missed over the last 3 years.[15 POINTS]
Salary ranking 11 10 8 5 9 9 7 3
Absences 18 17 29 36 11 26 28 35
Salary ranking 11 8 7 2 9 8 6 3
Absences 14 20 32 39 16 26 31 40
Construct a scatter diagram for these data and indicate the type of relationship.
ANSWER:
5. A study by the Atlanta, Georgia, Department of Transportation on the effect of bus ticket prices on the number of passengers produced the following results:
Ticket price (cents)
25 30 35 40 45 50 55 60
Passengers per 100 miles
800 780 780 660 640 600 620 620
a. Plot these data.[5 POINTS]
ANSWER:
b. Develop the estimating equation that best describes these data.[10 POINTS]
ANSWER:
c. Predict the number of passengers per 100 miles if the ticket price were 70 cents.[5 POINTS]
ANSWER:
6. A financial consultant is interested in the differences in capital structure within different firm sizes in a certain industry. The consultant surveys a group of firms with assets of different amounts and divides the firms into three groups. Each firm is classified according to whether its total debt is greater than stockholders’ equity or whether its total debt is less than stockholders’ equity. The results of the survey are:
Firm Asset Size (in $ thousands)
<500 500-2,000 2,000 + Total
Debt < equity 7 10 8 25
Debt > equity 10 18 9 37
Total 17 28 17 62
Do the three firm sizes have the same capital structure? Use the 0.10 significance level.[15 POINTS]
ANSWER:
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