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 535 customer sales invoices shows that 159 out of 535 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)No/Yes , the entire interval (Click to select)is/is not above .20.

Answer 1

Sample size, n = 535

Favorable outcome, x = 159

Sample proportion, p̄ = x/n = 0.2972

95% Confidence interval :  

At α = 0.05, two tailed critical value, z_c = NORM.S.INV(0.05/2) = 1.96

Lower Bound = p̄ - z_c*√( p̄ *(1- p̄ )/n) = 0.2972 - 1.96 *√(0.2972*0.7028/535) = 0.258

Upper Bound = p̄ + z_c*√( p̄ *(1- p̄ )/n) = 0.2972 + 1.96 *√(0.2972*0.7028/535) = 0.336

The 95 percent confidence interval is (0.258, 0.336).

Yes , the entire interval is above 0.20.