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.

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Asked Nov 21, 2019
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 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. 

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Expert Answer

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From the given information, it can be observed that The both samples are selected using simple random sampling The sample are independent of each other Each sample includes at least ten failures and ten successes. Hence, all the assumptions are satisfied

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The level of confidence is 0.95. The critical value using standard normal table is 1.96. The confidence interval is obtained as follows:

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1 п, п, 1 n2 п, CI = п п, п n2 93 1 250 44 44 93 93 44 250 250 250 0.05 250 250 250 250 2 0.196 ±1.96(0.0389) = 0.196 ± 0.0763 =(0.1197,0.2723)

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