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10.18 A large retail lawn care dealer currently provides a 2-year warranty on all lawn mowerssold at its stores. A new employee suggested that the dealer could save money by just not offeringthe warranty. To evaluate this suggestion, the dealer randomly decides whether or not to offerthe warranty to the next 50 customers who enter the store and express an interest in purchasinga lawnmower. Out of the 25 customers offered the warranty, 10 purchased a mower as comparedto 4 of 25 not offered the warranty.a. Place a 95% confidence interval on π,-T2, the difference in the proportions ofcustomers purchasing lawnmowers with and without the warranty.b. Test the research hypothesis that offering the warranty will increase the propor-tion of customers who will purchase a mower. Use α-,05.

Question
10.18 A large retail lawn care dealer currently provides a 2-year warranty on all lawn mowers
sold at its stores. A new employee suggested that the dealer could save money by just not offering
the warranty. To evaluate this suggestion, the dealer randomly decides whether or not to offer
the warranty to the next 50 customers who enter the store and express an interest in purchasing
a lawnmower. Out of the 25 customers offered the warranty, 10 purchased a mower as compared
to 4 of 25 not offered the warranty.
a. Place a 95% confidence interval on π,-T2, the difference in the proportions of
customers purchasing lawnmowers with and without the warranty.
b. Test the research hypothesis that offering the warranty will increase the propor-
tion of customers who will purchase a mower. Use α-,05.
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10.18 A large retail lawn care dealer currently provides a 2-year warranty on all lawn mowers sold at its stores. A new employee suggested that the dealer could save money by just not offering the warranty. To evaluate this suggestion, the dealer randomly decides whether or not to offer the warranty to the next 50 customers who enter the store and express an interest in purchasing a lawnmower. Out of the 25 customers offered the warranty, 10 purchased a mower as compared to 4 of 25 not offered the warranty. a. Place a 95% confidence interval on π,-T2, the difference in the proportions of customers purchasing lawnmowers with and without the warranty. b. Test the research hypothesis that offering the warranty will increase the propor- tion of customers who will purchase a mower. Use α-,05.

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check_circleAnswer
Step 1

a.

Confidence Interval:

The form of the confidence interval is,

CI = Point estimate ± Margin of error

The approximate 100*(1–α)% confidence interval for the difference between two population proportions (π1– π2) will be obtained using the formula given below:

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Step 2

Obtain the sample proportion of customers purchasing lawnmowers with warranty:

It is given that among a sample of 25 customers offered the warranty, 10 customers purchased a lawnmower.

The sample size is n1 = 25.

The number of specified characteristics is x1 = 10.

The sample proportion of customers purchasing lawnmowers with warranty is obtained as 0.4 from the calculation given below:

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Step 3

Obtain the sample proportion of customers purchasing lawnmowers without warranty:

It is given that among a sample of 25 customers not offered the warranty, 4 customers purchased a lawnmower.

The sample size is n2 = 25.

The number of s...

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