Wierzycaz

2020-10-28

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 who expressed interest in buying a tractor, 250 were randomly offered a warranty, and the rest did not receive. Ninety-three of those offering a warranty, and fifty-four of those not offering a warranty ended up buying a tractor.

a. Construct a$95\mathrm{\%}$ 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 a manager offer a warranty based on this test?

a. Construct a

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 a manager offer a warranty based on this test?

Caren

Skilled2020-10-29Added 96 answers

Step 1

a)

All necessary assumptions are met:

The sampling method for each population is simple random sampling.

Independent samples.

Each sample includes at least 10 successes and 10 failures.

Proportion of customers purchasing tractors with warranties

Proportion of customers purchasing tractors without warranties

Difference in proportions

Pooled sample proportion

The standard error (SE) of the sampling distribution difference between two proportions.

where p is the pooled sample proportion,

Step 2

z value for

Margin of error

For

b)

Formulating Hypothesis

Null :

Alternate : Ha: Offering the warranty increases the proportion of customers who eventually purchase a tractor.

Calculating Test statistic z :

Decision about the null hypothesis

At 0.05 significance level

Since it is observed that

Using the P-value approach: The p-value is

Conclusion :

Offering the warranty increases the proportion of customers who eventually purchase a tractor.

Yes, they should offer a guarantee