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 504 customer sales invoices shows that 156 out of 504 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.) The 95 percent confidence interval is [, ]. , the entire interval above .20.

Answer 1

proportion p(hat) = 156/504 =0.31

sample size n = 504

z score for 95% confidence interval is z = 1.96 (using z distribution table)

using the formula for confidence interval

setting the values, we get

this gives

this gives us

CI = (0.270, 0.350)

Yes, we are 95% confident that this proportion exceeds 0.20 because 95% confidence interval lower limit and higher limits are above 0.20 proportion. So, we can say that the entire confidence interval is above 0.20.