Use the following information for Q$1$ through Q$5.$

$($p$\mathrm{.}288,$ q$9\mathrm{.}29)$ An insurance company has the business objective of reducing the amount of time it takes to approve applications for

life insurance. The approval process consists of underwriting, which includes a review of the application, a medical information

bureau check, possible requests for additional medical information and medical exams, and a policy compilation state in which the

policy pages are generated and sent for delivery. The ability to deliver approved policies to customers in a timely manner is critical

to the profitability of this service. During a period of one month, you collect a random sample of $27$ approved policies and the total

processing time, in days, and the summary statistic is presented as below. In the past, the average processing time was $45$ days. At

the $0\mathrm{.}05$ level of significance, is there evidence that the mean processing time has been reduced?

What would be the proper alternative hypothesis?

Prompts

Parameter to test

expected relationship

$(3)$ Benchmark

Answers

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