14.4 Biometrics is a technology that helps identify people by facial and body features and is used by banks to reduce fraud. If in 15 trails the machine correctly identified 10 people, test the hypothesis that the machine’s identification rate is 50%

14.8 In a regression analysis, 12 out of 30 residuals are greater than 1.00 in value, and the rest are not. With A denoting a residual greater than 1 and B a residual less than 1, the residuals are as follows:

B B B B B B B B B A A A A A A A A A A B B B B B B B B B A A

Do you believe that the regression errors are random? Explain.

14.14 Following reports by scientists that a large hole in the atmospheric ozone revolves around Antarctica, two U.S. jets of the U-2 type were sent to collect samples of air for comparison with samples collected elsewhere, to see if the ozone layer is indeed depleted. If so, controls on the manufacture of ozone-depleting fluorocarbons would have to be imposed to prevent further dangerous depletion of ozone around the world. Using the following data, test the null hypothesis that the ozone concentration over Antarctica is approximately equal to the concentration found in other areas against the alternative hypothesis that the concentration over Antarctica is lower than found elsewhere.

Antarctica (%): 6, 10, 12, 23, 11, 31, 25, 11, 8, 7, 34, 14, 16, 18, 40, 31, 22, 5

Other places (%) 17, 32, 41, 29, 16, 30, 19, 51, 65, 22, 40, 47, 29, 30, 16, 70

14.46 A company is considering five possible names for its new product. Before choosing a name, the firm decides to test whether all five names are equally appealing. A random sample of 100 people is chosen, and each person is asked to state her or his choice of the best name among the five possibilities. The numbers of people who chose each one of the names are as follows:

Name: A B C D E

Number of Choices: 4 12 34 40 10

Conduct the test.

14.34 A researcher at an accounting firm wants to out whether the current ratio for three industries is about the same. Random samples of eight firms in industry A, six firms in industry B, and six firms in industry C are available. The ratios are as follows:

Industry A: 1.38, 1.55, 1.90, 2.00, 1.22, 2.11, 1.98, 1.61

Industry B: 2.33, 2.50, 2.79, 3.01, 1.99, 2.45

Industry C: 1.06, 1.37, 1.09, 1.65, 1.44, 1.11

Conduct the test at \(\alpha \) = 0.05, and state your conclusion.

15.4 The company that marketed the Yugoslav car Yugo in the United States needed to estimate the proportion of the market that the car would capture once it was introduced. Based on experience with Korean, French, and other foreign cars marked in the country, one of the company’s executives gave his prior probability distribution of the proportion of the foreign-car market that would go to Yugo. The prior probability distribution of this proportion ( M = market share) is as follows:

M P(M)

0.05 0.3

0.15 0.5

0.20 0.1

0.25 0.1

A random sample of 18 potential buyers of new foreign cars revealed that 1 of them would buy a Yugo. Compute the posterior probability distribution of M.

15.12 Video Dog is an ingenious invention. It allows you to enjoy the pleasures of owning a pet without having to feed it, take it for walks, or worry about fleas and ticks. Before marketing the idea, the manufacturer wanted to estimate average monthly sales that would result in an area with a given population. From experience with similar products (probably the pet rock), the manufacturer assessed a normal prior probability distribution for average monthly sales in the area, with mean 15,000 and standard deviation 4, 000. A random sample of 12 monthly sales in an area of about the same population and in the same geographic region gave a mean of 9,867 and a standard deviation of 1,055. Give a 95% highest-posterior-density credible set for the average monthly sales the manufacturer may expect in a region of the given size. Assume sales are normally distributed.

15.24 Boeing has drawn up plans for a new fuel-saving jet, the 7J7, that is designed to compete with the European-built Airbus 320. Boeing is currently conducting research to assess the feasibility of building the 7J7. Company experts believe there is a 0.20 chance that sales of the new plane would bring in gross revenues of $400 million over a period of 2 years; a 0.30 chance that sales of the plane during this period would bring in $300 million; and a 0.50 chance that sales would bring in only $200 million. Were Boeing not to manufacture the plane and instead use its resources to make other planes that are currently being used by airlines all over the world, there is a 0.75 chance that sales of these other planes during the period in question will bring in gross revenues of $250 million, and a 0.25 chance that sales will bring in $300 million. Draw a decision tree for this problem, and solve it. What should Boeing do?

16.4 A financial analyst is interested in estimating the average amount of a foreign loan by U.S. banks. The analyst believes that the amount of a loan may be different depending on the bank, or, more precisely, on the extent of the bank’s involvement in foreign loans. The analyst obtains the following data on the percentage of profits of U.S. banks from loans to Mexico and proposes to use these data in the construction of stratum weights. The strata are the different banks: First Chicago, 33%; Manufacturers Hanover, 27%; Bankers Trust, 21%; Chemical Bank, 19%; Wells Fargo Bank, 19%;

Citicorp, 16%; Mellon Bank, 16%; Chase Manhattan, 15%; Morgan Guarantee Trust, 9%.

1. Construct the stratum weights for proportional allocation.
2. Discuss two possible problems with this study.

16.8 Recently a survey was conducted to assess the quality of investment brokers.

A random sample of 6 brokerage houses was selected from a total of 27 brokerage houses. Each of the brokers in the selected brokerage houses was evaluated by an independent panel of industry experts as "highly qualified" (HQ) or was given an evaluation below this rating. The designers of the survey wanted to estimate the proportion of all brokers in the entire industry who would be considered highly qualified. The survey results are in the following table.

Brokerage House Total Number of Brokers Number of HQ Brokers

1 120 80

2 150 75

3 200 100

4 100 65

5 88 45

6 260 200

Use the cluster sampling estimator of the population proportion to estimate the proportion of all highly qualified brokers in the investment industry. Also give a 99% confidence interval for the population proportion you estimated.

16.10 A tire manufacturer maintains strict quality control of its tire production.

This entails frequent sampling of tires from large stocks shipped to retailers. Samples of tires are selected and run continuously until they are worn out, and the average number of miles "driven" in the laboratory is noted. Suppose a warehouse contains 11,000 tires arranged in a certain order. The company wants to select a systematic sample of 50 tires to be tested in the laboratory. Use randomization to determine the first item to be sampled, and give the rule for obtaining the rest of the sample in this case.

1. A population is composed of 100 items arranged in some order. Every stratum of 10 items in the order of arrangement tends to be similar in its values. An "every 10th" systematic sample is selected. The first item, randomly chosen, is the 6th item, and its value is 20. The following items in the sample are, of course, the 16th, the 26th, etc. The values of all items in the systematic sample are as follows: 20, 25, 27, 34, 28, 22, 28, 21, 37, 31. Give a 90% confidence interval for the population mean.

Price: $43.48

Solution: The downloadable solution consists of 18 pages, 2548 words and 2 charts.
Deliverable: Word Document