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Problem Set 5 1) Complete exercise...

Problem Set 5

1) Complete exercise 7.11, 7.15, 7.27 (parts a and c only),

7.11 A simple random sample of n = 300 full-time employees is selected from a company list containing the names of all N = 5,000 full-time employees in order to evaluate job satisfaction.

A. Give an example of possible coverage error.

C, Give an example of possible sampling error.

7.15 Given a normal distribution with µ= 100 and ð = 10, if you select a sample of n = 25 , what is the probability that is

a. less than 95?

c. above 102.2?

7.27 You plan to conduct a marketing experiment in which students are to taste one of two different brands of soft drink. Their task is to correctly identify the brand tasted. You select a random sample of 200 students and assume that the students have no ability to distinguish between the two brands.

(Hint: If an individual has no ability to distinguish between the two soft drinks, then each brand is equally likely to be selected.)

a. What is the probability that the sample will have between 50% and 60% of the identifications correct?

c. What is the probability that the sample percentage of correct identifications is greater than 65%?

SET 2) Complete exercises 8.1, 8.9, 8.11, 8.13, 8,27 (parts a and b only), 8.33, 8.35

LEARNING THE BASICS

8.1 If ̅Ẋ = 85, ð = 8, and n = 64 construct a 95% confidence interval estimate of the population mean, µ.

8.9 Assuming that the population is normally distributed, construct a 95% confidence interval estimate for the population mean for each of the following samples:

Sample A: 1, 1, 1, 1, 8, 8, 8, 8

Sample B: 1, 2, 3, 4, 5, 6, 7, 8

Explain why these two samples produce different confidence intervals even though they have the same mean and range.

8.11 A stationery store wants to estimate the mean retail value of greeting cards that it has in its inventory. A random sample of 100 greeting cards indicates a mean value of $2.55 and a standard deviation of $0.44.

a. Assuming a normal distribution, construct a 95% confidence interval estimate of the mean value of all greeting cards in the store’s inventory.

b. Suppose there were 2,500 greeting cards in the store’s inventory. How are the results in (a) useful in assisting the store owner to estimate the total value of her inventory?

8.13 The U.S. Department of Transportation requires tire manufacturers to provide tire performance information on the sidewall of the tire to better inform prospective customers when making purchasing decisions. One very important measure of tire performance is the tread wear index, which indicates the tire’s resistance to tread wear compared with a tire graded with a base of 100. This means that a tire with a grade of 200 should last twice as long, on average, as a tire graded with a base of 100. A consumer organization wants to estimate the actual tread wear index of a brand name of tires that claims “graded 200” on the sidewall of the tire. A random

of indicates a sample mean tread wear index of 195.3 and a sample standard deviation of 21.4.

a. Assuming that the population of tread wear indexes is normally distributed, construct a 95% confidence interval estimate of the population mean tread wear index for tires produced by this manufacturer under this brand name.

b. Do you think that the consumer organization should accuse the manufacturer of producing tires that do not meet the performance information provided on the sidewall of the tire? Explain.

8.27 The start of the twenty-first century saw many corporate scandals and many individuals lost faith in business. In a 2007 poll conducted by the New York City-based Edelman

Public Relations firm, 57% of respondents say they trust business to “do what is right.” This percentage was the highest in the annual survey since 2001 (data extracted from

G. Colvin, “Business is Back!” Fortune, May 14, 2007, pp.40–48).

a. Construct a 95% confidence interval estimate of the population proportion of individuals who trust business to “do what is right” assuming that the poll surveyed:

1. 100 individuals.

2. 200 individuals.

3. 300 individuals.

b. Discuss the effect that sample size has on the width of confidence intervals.

8.33 If you want to be 95% confident of estimating the population proportion to within a sampling error of and there is historical evidence that the population proportion is approximately 0.40, what sample size is needed?

8.35 If the manager of a paint supply store wants to estimate the mean amount of paint in a 1-gallon can to within ±0.004 gallon with 95% confidence and also assumes that the standard deviation is 0.02 gallon, what sample size is needed?

1) Complete exercise 7.11, 7.15, 7.27 (parts a and c only),

7.11 A simple random sample of n = 300 full-time employees is selected from a company list containing the names of all N = 5,000 full-time employees in order to evaluate job satisfaction.

A. Give an example of possible coverage error.

C, Give an example of possible sampling error.

7.15 Given a normal distribution with µ= 100 and ð = 10, if you select a sample of n = 25 , what is the probability that is

a. less than 95?

c. above 102.2?

7.27 You plan to conduct a marketing experiment in which students are to taste one of two different brands of soft drink. Their task is to correctly identify the brand tasted. You select a random sample of 200 students and assume that the students have no ability to distinguish between the two brands.

(Hint: If an individual has no ability to distinguish between the two soft drinks, then each brand is equally likely to be selected.)

a. What is the probability that the sample will have between 50% and 60% of the identifications correct?

c. What is the probability that the sample percentage of correct identifications is greater than 65%?

SET 2) Complete exercises 8.1, 8.9, 8.11, 8.13, 8,27 (parts a and b only), 8.33, 8.35

LEARNING THE BASICS

8.1 If ̅Ẋ = 85, ð = 8, and n = 64 construct a 95% confidence interval estimate of the population mean, µ.

8.9 Assuming that the population is normally distributed, construct a 95% confidence interval estimate for the population mean for each of the following samples:

Sample A: 1, 1, 1, 1, 8, 8, 8, 8

Sample B: 1, 2, 3, 4, 5, 6, 7, 8

Explain why these two samples produce different confidence intervals even though they have the same mean and range.

8.11 A stationery store wants to estimate the mean retail value of greeting cards that it has in its inventory. A random sample of 100 greeting cards indicates a mean value of $2.55 and a standard deviation of $0.44.

a. Assuming a normal distribution, construct a 95% confidence interval estimate of the mean value of all greeting cards in the store’s inventory.

b. Suppose there were 2,500 greeting cards in the store’s inventory. How are the results in (a) useful in assisting the store owner to estimate the total value of her inventory?

8.13 The U.S. Department of Transportation requires tire manufacturers to provide tire performance information on the sidewall of the tire to better inform prospective customers when making purchasing decisions. One very important measure of tire performance is the tread wear index, which indicates the tire’s resistance to tread wear compared with a tire graded with a base of 100. This means that a tire with a grade of 200 should last twice as long, on average, as a tire graded with a base of 100. A consumer organization wants to estimate the actual tread wear index of a brand name of tires that claims “graded 200” on the sidewall of the tire. A random

of indicates a sample mean tread wear index of 195.3 and a sample standard deviation of 21.4.

a. Assuming that the population of tread wear indexes is normally distributed, construct a 95% confidence interval estimate of the population mean tread wear index for tires produced by this manufacturer under this brand name.

b. Do you think that the consumer organization should accuse the manufacturer of producing tires that do not meet the performance information provided on the sidewall of the tire? Explain.

8.27 The start of the twenty-first century saw many corporate scandals and many individuals lost faith in business. In a 2007 poll conducted by the New York City-based Edelman

Public Relations firm, 57% of respondents say they trust business to “do what is right.” This percentage was the highest in the annual survey since 2001 (data extracted from

G. Colvin, “Business is Back!” Fortune, May 14, 2007, pp.40–48).

a. Construct a 95% confidence interval estimate of the population proportion of individuals who trust business to “do what is right” assuming that the poll surveyed:

1. 100 individuals.

2. 200 individuals.

3. 300 individuals.

b. Discuss the effect that sample size has on the width of confidence intervals.

8.33 If you want to be 95% confident of estimating the population proportion to within a sampling error of and there is historical evidence that the population proportion is approximately 0.40, what sample size is needed?

8.35 If the manager of a paint supply store wants to estimate the mean amount of paint in a 1-gallon can to within ±0.004 gallon with 95% confidence and also assumes that the standard deviation is 0.02 gallon, what sample size is needed?

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