Exercises

Write the answers to the following questions from the textbook. Submit all answers as a single document.

Problem 10.63

The pet-drug market is growing very rapidly. Before new pet drugs can be introduced into the market place, they must be approved by the FDA. In 1999, the Novartis Company was trying to get Anafranil, a drug to reduce dog anxiety, approved. According to an article (E. Tanouye, "The Ow in Bowwow: With Growing Market in Pet Drugs, Makers Revamp Clinical Trials," The Wall Street Journal , April 13, 1999), Novartis had t find a way to translate a dog’s anxiety symptoms into numbers that could be used to prove to the FDA that the drug had a statistically significant effect on the condition.

1. What is meant by the phrase statistically significant effect?
2. Consider an experiment in which dogs suffering from anxiety are divided into two groups. One group will be given Anafranil, and the other will be given a placebo (that is, a drug without active ingredients). How can you translate a dog’s anxiety symptoms into numbers? In other words, define a continuous variable, X1, the measurement of effectiveness of the drug Anafranil, and X2, the measurement of the effectiveness of the placebo.
3. Building on your answer to part (b), define the null and alternative hypotheses for this study.

Problem 11.36

The operations manager for an appliance manufacturer wants to determine the optimal length of time for the washing cycle of a household clothes washer. An experiment is designed to measure the effect of detergent brand and washing cycle time on the amount of dirt removed from standard household laundry loads. Four brands of detergent (A, B, C, D) and four levels of washing cycle (18, 20, 22, and 24 minutes) are specifically selected for analysis. In order to run the experiment, 32 standard house-hold laundry loads (having equal weight and dirt) are randomly assigned, 2 each, to the 16 detergent-washing cycle time combinations. The results, in pounds of dirt removed (stored in the laundry.xls file), are as follows:

WASHING CYCLE TIME (IN MINUTES)

DETERGENT BRAND 18 20 22 24

A 0.11 0.13 0.17 0.17

0.09 0.13 0.19 0.18

B 0.12 0.14 0.17 0.19

0.10 0.15 0.18 0.17

C 0.08 0.16 0.18 0.20

0.09 0.13 0.17 0.16

D 0.11 0.12 0.16 0.15

0.13 0.13 0.17 0.17

At the 0.05 level of significance,

1. Is there an interaction between detergent and washing cycle time?
2. Is there an effect due to detergent brand?
3. Is there an effect due to washing cycle time?
4. Plot the mean amount of dirt removed (in pounds) for each detergent brand for each washing cycle time.
5. If appropriate, use the Tukey procedure to determine differences between detergent brands and between washing times.
6. What washing cycle should be used for this type of household clothes washer?
7. Repeat the analysis, using washing cycle time as the only factor. Compare your results to those of ( c ), ( e ), and ( f ).

Problem 12.67

A company that produces and markets videotaped continuing education programs for the financial industry has traditionally mailed sample tapes that contain previews of the programs to prospective customers. Customers then agree to purchase the program tapes or return the sample tapes. A group of sales representatives studied how to increase sales and found that many prospective customers believed it was difficult to tell from a sample tape alone whether the educational programs would meet their needs. The sales representatives performed an experiment to test whether sending the complete program tapes for review by customers would increase sales. They selected 80 customers from the mailing list and randomly assigned 40 t receive the sample tapes and 40 to receive the full-program tapes for review. They then determined the number of tapes that were purchased and returned in each group. The results of the experiment are as follows:

TYPE OF VIDEOTAPE RECEIVED

ACTION Sample Full Total

Purchased 6 14 20

Returned 34 26 60

Total 40 40 80

1. At the 0.05 level of significance, is there evidence of a difference in the proportion of tapes purchased on the basis of the type of tape sent to the customer?
2. On the basis of the results of ( a ), which tape do you think a representative should send in the future? Explain the rationale for your decision.
   The sales representatives also wanted to determine which of three initial sales approaches result in the most sales: ( 1 ) a video sales-information tape mailed to prospective customers, ( 2 ) a personal sales call to prospective customers, and (3 ) a telephone call to prospective customers.
   A random sample of 300 prospective customers was selected, and 100 were randomly assigned to each of the three sales approaches. The results, in terms of purchases of the full-program tapes, are as follows:
   SALES APPROACH
   ACTION Videotape Personal Sales Call Telephone Total
   Purchase 19 27 14 60
   Don’t purchase 81 73 86 240
   Total 100 100 100 300
3. At the 0.05 level of significance, is there evidence of a difference in the proportion of tapes purchased on the basis of the sales strategy used?
4. If appropriate, use the Marascuilo procedure and a=0.05 to determine which sales approach are different.
5. On the basis of the results of ( c ) and ( d ), which sales approach do you think a representative should use in the future? Explain the rationale for your decision.

Problem 13.74

Management of a soft-drink bottling company wants to develop a method for allocation delivery costs to customers. Although one cost clearly relates to travel time within a particular route, another variable cost reflects the time required to unload the cases of soft drink at the delivery point. A sample of 20 deliveries within a territory

was selected. The delivery times and the numbers of cases delivered were recorded in the delivery.xls file:

Customer # of Cases Delivery time (min)

1 52 32.1

2 64 34.8

3 73 36.2

4 85 37.8

5 95 37.8

6 103 39.7

7 116 38.5

8 121 41.9

9 143 44.2

10 157 47.1

11 161 43.0

12 184 49.4

13 202 57.2

14 218 56.8

15 243 60.6

16 254 61.2

17 267 58.2

18 275 63.1

19 287 65.6

20 298 67.3

Develop a regression model to predict delivery time, based on the number of cases delivered.

1. Use the least-squares method to compute the regression coefficients b0 and b1 in this problem.
2. Interpret the meaning of b0 and b1 in this problem.
3. Predict the delivery time for 150 cases of soft drink.
4. Should you use the model to predict the delivery time for a customer who is receiving 500 cases of soft drink? Why or why not?
5. Determine the coefficient of determination, r2, and explain its meaning in this problem.
6. Perform a residual analysis. Is there any evidence of a pattern in the residuals? Explain.
7. At the 0.05 level of significance, is there evidence of a linear relationship between delivery time and the number of cases delivered?
8. Construct a 95% confidence interval estimate of the mean delivery time for 150 cases of soft drink.
9. Construct a 95% prediction interval of the delivery time for a single delivery of 150 cases of soft drink.
10. Construct a 95% confidence interval estimate of the population slope.

Explain how the results in ( a ) through ( j ) can help allocate delivery costs to customers.

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Solution: The downloadable solution consists of 20 pages, 1893 words and 15 charts.
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