Consumer Reports (January 2005) indicates that profit margins on extended warran

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 475 customer sales invoices shows that 152 out of 475 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

Explanation / Answer

z-values are taken from standard z-table.

95% CI = (0.278, 0.362)

As this CI lies above 0.20, we are 95% confidentt that the proportion exceeds 0.2

n 475 p 0.32 z-value of 95% CI 1.9600 SE = sqrt(p*(1-p)/n) 0.02140 ME = z*SE 0.04195 Lower Limit = p - ME 0.27805 Upper Limit = p + ME 0.36195 95% CI (0.2781 , 0.3619 )

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