Efficiency of Ultra-Green Cars A car manufacturer advertises that its new ultra-green car obtains an average...

Transcribed Image Text:

Efficiency of "Ultra-Green" Cars A car manufacturer advertises that its new "ultra-green" car obtains an average of 100 miles per gallon (mpg) and, based on its fuel emissions, is one of the few cars that earns an A+ rating from the Environmental Protection Agency. Jared Beane, an analyst at Pinnacle Research, records the mpg for a sample of 25 "ultra-green" cars after the cars were driven equal distances under identical conditions. Table 8.1 shows a portion of the data. FILE MPG TABLE 8.1 MPG for a Sample of 25 "Ultra-Green" Cars MPG 97 117 98 Jared would like to make statistical inferences regarding key population parameters. In particular, he wants to use the sample information to 1. Estimate the mean mpg of all ultra-green cars with 90% confidence. 2. Estimate the proportion of all ultra-green cars that obtain over 100 mpg with 90% confidence. 3. Determine the sample size that will enable him to achieve a specified level of precision in his mean and proportion estimates. A synopsis of this case is provided at the end of Section 8.4. SYNOPSIS OF INTRODUCTORY CASE Jared Beane, an analyst at a research firm, prepares to write a report on the new ultra-green car that boasts an average of 100 mpg. Based on a sample of 25 cars, Jared reports, with 90% confidence, that the average mpg of all ultra-green cars is between 92.86 mpg and 100.18 mpg. Jared also constructs the 90% confidence interval for the proportion of cars that obtain more than 100 mpg and reports the interval between 0.132 and 0.428. Jared wishes to increase the precision of his confidence intervals by reducing the margin of error. If his desired margin of error is 2 mpg for the population mean, he must use a sample of at least 75 cars for the analysis. Jared also wants to reduce the margin of error to 0.10 for the proportion of cars that obtain more than 100 mpg. Using a conservative estimate, he calculates that a sample of at least 68 cars is needed to achieve this goal. Thus, in order to gain precision in the interval estimate for both the mean and the proportion with 90% confidence, Jared's sample must contain at least 75 cars. Efficiency of "Ultra-Green" Cars A car manufacturer advertises that its new "ultra-green" car obtains an average of 100 miles per gallon (mpg) and, based on its fuel emissions, is one of the few cars that earns an A+ rating from the Environmental Protection Agency. Jared Beane, an analyst at Pinnacle Research, records the mpg for a sample of 25 "ultra-green" cars after the cars were driven equal distances under identical conditions. Table 8.1 shows a portion of the data. FILE MPG TABLE 8.1 MPG for a Sample of 25 "Ultra-Green" Cars MPG 97 117 98 Jared would like to make statistical inferences regarding key population parameters. In particular, he wants to use the sample information to 1. Estimate the mean mpg of all ultra-green cars with 90% confidence. 2. Estimate the proportion of all ultra-green cars that obtain over 100 mpg with 90% confidence. 3. Determine the sample size that will enable him to achieve a specified level of precision in his mean and proportion estimates. A synopsis of this case is provided at the end of Section 8.4. SYNOPSIS OF INTRODUCTORY CASE Jared Beane, an analyst at a research firm, prepares to write a report on the new ultra-green car that boasts an average of 100 mpg. Based on a sample of 25 cars, Jared reports, with 90% confidence, that the average mpg of all ultra-green cars is between 92.86 mpg and 100.18 mpg. Jared also constructs the 90% confidence interval for the proportion of cars that obtain more than 100 mpg and reports the interval between 0.132 and 0.428. Jared wishes to increase the precision of his confidence intervals by reducing the margin of error. If his desired margin of error is 2 mpg for the population mean, he must use a sample of at least 75 cars for the analysis. Jared also wants to reduce the margin of error to 0.10 for the proportion of cars that obtain more than 100 mpg. Using a conservative estimate, he calculates that a sample of at least 68 cars is needed to achieve this goal. Thus, in order to gain precision in the interval estimate for both the mean and the proportion with 90% confidence, Jared's sample must contain at least 75 cars.