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Data Analysis for Modeling

Five years ago, an automobile manufacturer stated offering an extended warranty to buyers of its sport-utility vehicle. The extended warranty covered defects occurring after the initial three-year warranty expired. Of the 10,000 people who bought the sport-utility in the first year of the program,15 percent purchased the extended warranty. In the Warranty Department, you have recently received data on a random sample of 200 of the cards sold in the first year that the extended warranty was available. For this sample, the average extended warranty expenditure per car for the one-year period after the initial warranty elapsed was $350, with a standard deviation of $100.

a. What is a 95 percent confidence interval for the mean one-year extended-warranty expenditure per automobile?

b. At its introduction, the extended warranty was priced at$445per year per automobile. Compute a95 percent confidence interval for the one-year profitability of the extended warranty.

c. How large a same would the Warranty Department require if it wanted its95 percent confidence interval for the mean warranty expenditure to be no more than + $5?

Solution Preview

Statistics rely on probability. Whenever you're given a mean of a sample, you don't really know if the true mean for the whole population is higher or lower than that sample mean. The confidence interval is a statistical calculation we can make to determine how likely it is that the true mean lies between two values, one above and one below the sample mean. Given a sample mean of 350, a sample size of ...