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 527 customer sales invoices shows that 167 out of 527 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 [   , ].

(Click to select)Yes or No , the entire interval (Click to select)is not or is above .20.

Answer 1

to find the confidence interval for the population proportion, we need to find the point estimate of the population proportion.

The point estimate for the proportion of digital camera customers purchased the new warranty is

The 9%% confidence interval for the population proportion of digital camera customers that purchased the new warranty is

for 95% confidence

Yes we can be 95% sure that this proportion exceeds 0.20 as the lower limit of the confidence interval is greater than 0.20.