manager at ACME Equipment Sale and Rental wondered how offering a free two-year service warranty on its tractors might influence sales. For the next 500 customers expressing interest in purchasing a tractor, 250 were randomly offered the warranty and the rest were not. Ninety-three of those offered the warranty, and fifty-four of those not offered the warranty eventually purchased a tractor. a. Construct a 95% confidence interval for the difference between the proportions of customers purchasing tractors with and without warranties. Be sure to check all necessary assumptions, and interpret the interval. b. Test the hypothesis that offering the warranty increases the proportion of customers who eventually purchase a tractor. Be sure to check all necessary assumptions, state the null and alternative hypotheses, obtain the p-value, and state your conclusion. Should the manager offer the warranty based on this test?
A manager at ACME Equipment Sale and Rental wondered how offering a free two-year service warranty on its tractors might influence sales. For the next 500 customers expressing interest in purchasing a tractor, 250 were randomly offered the warranty and the rest were not. Ninety-three of those offered the warranty, and fifty-four of those not offered the warranty eventually purchased a tractor.
a. Construct a 95% confidence interval for the difference between the proportions of customers purchasing tractors with and without warranties. Be sure to check all necessary assumptions, and interpret the interval.
b. Test the hypothesis that offering the warranty increases the proportion of customers who eventually purchase a tractor. Be sure to check all necessary assumptions, state the null and alternative hypotheses, obtain the p-value, and state your conclusion. Should the manager offer the warranty based on this test?
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