Question

Consumer Reports (January 2005) indicates that profit margins on extended warranties are much greater than on the purchase of most products. In this exercise we consider a major electronics retailer that wishes to increase the proportion of customers who buy extended warranties on digital cameras. Historically, 20 percent of digital camera customers have purchased the retailer’s extended warranty. To increase this percentage, the retailer has decided to offer a new warranty that is less expensive and more comprehensive. Suppose that three months after starting to offer the new warranty, a random sample of 525 customer sales invoices shows that 130 out of 525 digital camera customers purchased the new warranty. Find a 95 percent confidence interval for the proportion of all digital camera customers who have purchased the new warranty. Are we 95 percent confident that this proportion exceeds .20? (Round your answers to 3 decimal places.)

Answer 1

We need to construct the 95% confidence interval for the population proportion. We have been provided with the following information about the number of favorable cases:

Favorable Cases X=	130
Sample Size N =	525

The sample proportion is computed as follows, based on the sample size N=525 and the number of favorable cases X=130:

.

Therefore, based on the data provided, the 95% confidence interval for the population proportion is 0.211<p<0.285, which indicates that we are 95% confident that the true population proportion p exceeds 0.20

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