# Business Statistics 101

(1) If the number of miles per gallon achieved by all cars of a particular model has a mean of 25 and a standard deviation of 2, what is the probability that, for a random sample of 20 such cars, the average miles per gallon will be less than 24? Assume that the population distribution is normal.

(a) .0125

(b) .1443

(c) .2875

(d) .3026

(e) None of the above

(2) Suppose 1,600 of 2,000 registered voters said they plan to vote for the Republican candidate for president. Using the 0.95 degree of confidence, the population proportion lies within what interval?

(a) 69.2% to 86.4%

(b) 76.5% to 83.5%

(c) 77.7% to 82.3%

(d) 78.2% to 81.8%

(e) None of the above __________

(3) The mean weight of trucks traveling on the Virginia section of I-495 is not known. A state highway inspector needs an estimated mean. He selects 49 trucks passing the weighing station and finds the mean is 15.8 tons, with a standard deviation of the sample of 3.8 tons. Using the 0.95 degree of confidence, what is the confidence interval within which the population mean lies?

(a) 14.7 and 16.9

(b) 13.2 and 17.6

(c) 10.3 and 20.4

(d) 16.1 and 18.1

(e) None of the above __________

(4)The mean number of travel days per year for the outside salespeople employed by hardware distributors is to be estimated. The 0.90 degree of confidence is to be used. The mean of a small pilot study was 150 days, with a standard deviation of 14 days. If the population mean is to be estimated within two days, how many outside salespeople should be sampled?

(a) 134

(b) 452

(c) 511

(d) 1069

(e) None of the above __________

(5) The claim that "40% of those persons who retired from an industrial job before the age of 60 would return to work if a suitable job was available" is to be investigated at the 0.02 level of risk. If 74 out of the 200 workers sampled said they would return to work, what is our decision?

(a) Do not reject the null hypothesis because -0.866 lies in the region between 0 and -2.58

(b) Do not reject the null hypothesis because -0.866 lies in the region between 0 and -2.33

(c) Reject the null hypothesis because 37% is less than 40%

(d) Do not reject the null hypothesis because 37% lies in the area between 0 and 40%

(e) None of the above __________

(6) Suppose that an automobile manufacturer designed a radically new lightweight engine and wants to recommend the grade of gasoline to use. The four grades are below regular, regular, premium, and super premium. The test car made three trial runs on the test track using each of the four grades. Assuming any grade can be used at the 0.05 level, what is the critical value of F?

Kilometers per liter

Below Super

Trial # Regular Regular Premium Premium

1 39.31 36.69 38.99 40.04

2 39.87 40.00 40.02 39.89

3 39.87 41.01 39.99 39.93

(a) 1.96

(b) 2.33

(c) 4.07

(d) 12.00

(e) None of the above is correct __________

(7) In a study of foreign holdings in the U.S. banks, year-end share of assets in U.S. bank subsidiaries held by foreigners (as a percentage of total assets) was related to:

X1 = Annual change, in billions of dollars, in foreign direct investment in the U.S. (excluding finance, insurance, and real estate);

X2 = Bank price-earnings ratio;

X3 = Index of the exchange value of the dollar.

The regression results from the sample data gave the following population parameter estimates:

a = -3.248 b1= .101 b2= -.244 b3=.057 R2=.93

What is the estimated year-end share of assets in U.S. bank subsidiaries held by foreigners for a particular year if the annual change in foreign direct investment in the U.S., (excluding finance, insurance, and real estate) was $50 Billion, the bank price-earnings ratio was 12, and the index of exchange value of the dollar was 175?

(a) 3.456

(b) 8.849

(c) 12.097

(d) 15.672

(e) None of the above __________

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#### Solution Summary

This solution contains hand-written step-by-step instructions on how to answer seven in-depth multiple choice questions.

Business Statistics - Cars

(See attached file for full problem description)

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(1) If the number of miles per gallon achieved by all cars of a particular model has a mean of 25 and a standard deviation of 2, what is the probability that, for a random sample of 20 such cars, the average miles per gallon will be less than 24? Assume that the population distribution is normal.

(a) .0125

(b) .1443

(c) .2875

(d) .3026

(e) None of the above ______________

(2) Suppose 1,600 of 2,000 registered voters said they plan to vote for the Republican candidate for president. Using the 0.95 degree of confidence, the population proportion lies within what interval?

(a) 69.2% to 86.4%

(b) 76.5% to 83.5%

(c) 77.7% to 82.3%

(d) 78.2% to 81.8%

(e) None of the above __________

(3) The mean weight of trucks traveling on the Virginia section of I-495 is not known. A state highway inspector needs an estimated mean. He selects 49 trucks passing the weighing station and finds the mean is 15.8 tons, with a standard deviation of the sample of 3.8 tons. Using the 0.95 degree of confidence, what is the confidence interval within which the population mean lies?

(a) 14.7 and 16.9

(b) 13.2 and 17.6

(c) 10.3 and 20.4

(d) 16.1 and 18.1

(e) None of the above __________

(4)The mean number of travel days per year for the outside salespeople employed by hardware distributors is to be estimated. The 0.90 degree of confidence is to be used. The mean of a small pilot study was 150 days, with a standard deviation of 14 days. If the population mean is to be estimated within two days, how many outside salespeople should be sampled?

(a) 134

(b) 452

(c) 511

(d) 1069

(e) None of the above __________

(5) The claim that "40% of those persons who retired from an industrial job before the age of 60 would return to work if a suitable job was available" is to be investigated at the 0.02 level of risk. If 74 out of the 200 workers sampled said they would return to work, what is our decision?

(a) Do not reject the null hypothesis because -0.866 lies in the region between 0 and -2.58

(b) Do not reject the null hypothesis because -0.866 lies in the region between 0 and -2.33

(c) Reject the null hypothesis because 37% is less than 40%

(d) Do not reject the null hypothesis because 37% lies in the area between 0 and 40%

(e) None of the above __________

(6) Suppose that an automobile manufacturer designed a radically new lightweight engine and wants to recommend the grade of gasoline to use. The four grades are below regular, regular, premium, and super premium. The test car made three trial runs on the test track using each of the four grades. Assuming any grade can be used at the 0.05 level, what is the critical value of F?

Kilometers per liter

Below Super

Trial # Regular Regular Premium Premium

1 39.31 36.69 38.99 40.04

2 39.87 40.00 40.02 39.89

3 39.87 41.01 39.99 39.93

(a) 1.96

(b) 2.33

(c) 4.07

(d) 12.00

(e) None of the above is correct __________

(7) In a study of foreign holdings in the U.S. banks, year-end share of assets in U.S. bank subsidiaries held by foreigners (as a percentage of total assets) was related to:

X1 = Annual change, in billions of dollars, in foreign direct investment in the U.S. (excluding finance, insurance, and real estate);

X2 = Bank price-earnings ratio;

X3 = Index of the exchange value of the dollar.

The regression results from the sample data gave the following population parameter estimates:

a = -3.248 b1= .101 b2= -.244 b3=.057 R2=.93

What is the estimated year-end share of assets in U.S. bank subsidiaries held by foreigners for a particular year if the annual change in foreign direct investment in the U.S., (excluding finance, insurance, and real estate) was $50 Billion, the bank price-earnings ratio was 12, and the index of exchange value of the dollar was 175?

(a) 3.456

(b) 8.849

(c) 12.097

(d) 15.672

(e) None of the above __________

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(See attached file for full problem description)

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