# MATHEMATICS

 . Construct a 95% confidence interval for the population proportion of failures. (Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answers to 3 decimal places.)

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10.

 In a recent poll of 760 homeowners in the United States, one in five homeowners reports having a home equity loan that he or she is currently paying off. Using a confidence coefficient of 0.90, derive an interval estimate for the proportion of all homeowners in the United States that hold a home equity loan. Use Table 1. (Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answers to 3 decimal places.)

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11.

 An accounting professor is notorious for being stingy in giving out good letter grades. In a large section of 140 students in the fall semester, she gave out only 5% As, 23% Bs, 42% Cs, and 30% Ds and Fs. Assuming that this was a representative class, compute a 95% confidence interval of the probability of getting at least a B from this professor. Use Table 1. (Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answers to 3 decimal places.)

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12.

 You need to compute a 99% confidence interval for the population mean. How large a sample should you draw to ensure that the sample mean does not deviate from the population mean by more than 1.2? (Use 6.0 as an estimate of the population standard deviation from prior studies.) Use Table 1. (Round intermediate calculations to 4 decimal places and “z” value to 2 decimal places. Round up your answer to the nearest whole number.)

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13.

 In the planning stage, a sample proportion is estimated as   = 40/50 = 0.80. Use this information to compute the minimum sample size n required to estimate p with 99% confidence if the desired margin of error E = 0.12. What happens to n if you decide to estimate p with 90% confidence? Use Table 1. (Round intermediate calculations to 4 decimal places and “z” value to 2 decimal places. Round up your answers to the nearest whole number.)

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14.

 An analyst from an energy research institute in California wishes to precisely estimate a 99% confidence interval for the average price of unleaded gasoline in the state. In particular, she does not want the sample mean to deviate from the population mean by more than \$0.06. What is the minimum number of gas stations that she should include in her sample if she uses the standard deviation estimate of \$0.32, as reported in the popular press? Use Table 1. (Round intermediate calculations to 4 decimal places and “z” value to 2 decimal places. Round up your answer to the nearest whole number.)

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15.

 A student of business is interested in estimating a 99% confidence interval for the proportion of students who bring laptops to campus. He wishes a precise estimate and is willing to draw a large sample that will keep the sample proportion within five percentage points of the population proportion. What is the minimum sample size required by this student, given that no prior estimate of the population proportion is available?Use Table 1. (Round intermediate calculations to 4 decimal places and “z” value to 2 decimal places. Round up your answer to the nearest whole number.)

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