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3.1 A bank with a...

3.1 A bank with a branch located in a commercial district of a city has the business objective of developing an improved process for serving customers during the noon-to-1 P.M. lunch period. Management decides to first study the waiting time in the current process. The waiting time is defined as the time that elapses from when the customer enters the line until he or she reaches the teller window. Data are collected from a random sample of 15 customers, and the results (in minutes) are as follows:

4.21 5.55 3.02 5.13 4.77 2.34 3.54 3.20

4.50 6.10 0.38 5.12 6.46 6.19 3.79

Suppose that another branch, located in a residential area, is also concerned with improving the process of serving customers in the noon-to-1 P.M. lunch period. Data are collected from a random sample of 15 customers, and the results are as follows:

9.66 5.90 8.02 5.79 8.73 3.82 8.01 8.35

10.49 6.68 5.64 4.08 6.17 9.91 5.47

a. Assuming that the population variances from both banks are equal, is there evidence of a difference in the mean waiting time between the two branches? (Use 0.05)

b. Determine the p-value in (a) and interpret its meaning.

c. In addition to equal variances, what other assumption is necessary in (a)?

d. Construct and interpret a 95% confidence interval estimate of the difference between the population means in the two branches.

3.10 The manager of a paint supply store wants to determine whether the mean amount of paint contained in 1-gallon cans purchased from a nationally known manufacturer is actually 1 gallon. You know from the manufacturer’s specifications that the standard deviation of the amount of paint is 0.02 gallon. You select a random sample of 50 cans, and the mean amount of paint per 1-gallon can is 0.995 gallon.

a. Is there evidence that the mean amount is different from 1.0 gallon? (Use 0.01)

b. Compute the p-value and interpret its meaning.

c. Construct a 99% confidence interval estimate of the population mean amount of paint.

d. Compare the results of (a) and (c). What conclusions do you reach?

7.11 Recruiters are finding a wealth of unfiltered information about candidates on social-networking websites. A recent survey found that 83% of recruiters use search engines to learn more about candidates, and 43% eliminated candidates based on information they found (I. Phaneuf, “Who’s Googling You?” Job Postings, Spring 2009, pp. 12–13). What additional information would you want to know about a survey before you accepted the results of the study?

7.20 Suppose that you go to the drive-through window at Wendy’s and place an order. Two friends of yours independently place orders at the drive-through window at the same Wendy’s. Last month Wendy’s filled approximately 84.8% of orders correctly. What is the probability that

a. all three orders will be filled correctly?

b. none of the three will be filled correctly?

c. at least two of the three will be filled correctly?

d. What are the mean and standard deviation of the binomial distribution used in (a) through (c)? Interpret these values.

4.21 5.55 3.02 5.13 4.77 2.34 3.54 3.20

4.50 6.10 0.38 5.12 6.46 6.19 3.79

Suppose that another branch, located in a residential area, is also concerned with improving the process of serving customers in the noon-to-1 P.M. lunch period. Data are collected from a random sample of 15 customers, and the results are as follows:

9.66 5.90 8.02 5.79 8.73 3.82 8.01 8.35

10.49 6.68 5.64 4.08 6.17 9.91 5.47

a. Assuming that the population variances from both banks are equal, is there evidence of a difference in the mean waiting time between the two branches? (Use 0.05)

b. Determine the p-value in (a) and interpret its meaning.

c. In addition to equal variances, what other assumption is necessary in (a)?

d. Construct and interpret a 95% confidence interval estimate of the difference between the population means in the two branches.

3.10 The manager of a paint supply store wants to determine whether the mean amount of paint contained in 1-gallon cans purchased from a nationally known manufacturer is actually 1 gallon. You know from the manufacturer’s specifications that the standard deviation of the amount of paint is 0.02 gallon. You select a random sample of 50 cans, and the mean amount of paint per 1-gallon can is 0.995 gallon.

a. Is there evidence that the mean amount is different from 1.0 gallon? (Use 0.01)

b. Compute the p-value and interpret its meaning.

c. Construct a 99% confidence interval estimate of the population mean amount of paint.

d. Compare the results of (a) and (c). What conclusions do you reach?

7.11 Recruiters are finding a wealth of unfiltered information about candidates on social-networking websites. A recent survey found that 83% of recruiters use search engines to learn more about candidates, and 43% eliminated candidates based on information they found (I. Phaneuf, “Who’s Googling You?” Job Postings, Spring 2009, pp. 12–13). What additional information would you want to know about a survey before you accepted the results of the study?

7.20 Suppose that you go to the drive-through window at Wendy’s and place an order. Two friends of yours independently place orders at the drive-through window at the same Wendy’s. Last month Wendy’s filled approximately 84.8% of orders correctly. What is the probability that

a. all three orders will be filled correctly?

b. none of the three will be filled correctly?

c. at least two of the three will be filled correctly?

d. What are the mean and standard deviation of the binomial distribution used in (a) through (c)? Interpret these values.

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