Question

A fire insurance company thought that the mean distance from a home to the nearest fire department in a suburb of Chicago was at least 4.6 miles. It set its fire insurance rates accordingly. Members of the community set out to show that the mean distance was less than 4.6 miles. This, they thought, would convince the insurance company to lower its rates. They randomly indentified 61 homes and measured the distance to the nearest fire department from each. The resulting sample mean was 4.2. If σ = 2.8 miles, does the sample show sufficient evidence to support the community's claim at the α = .05 level of significance?

(a) Find z. (Give your answer correct to two decimal places.)

(b) Find the p-value. (Give your answer correct to four decimal places.)

The owner of a local chain of grocery stores is always trying to minimize the time it takes her customers to check out. In the past, she has conducted many studies of the checkout times, and they have displayed a normal distribution with a mean time of 12.8 minutes. and a standard deviation of 3 minutes. She has implemented a new schedule for cashiers in hopes of reducing the mean checkout time. A random sample of 25 customers visiting her store this week resulted in a mean of 11.9 minutes. Does she have sufficient evidence to claim the mean checkout time this week was less than 12.8 minutes? Use α = .02.

(c) Find z. (Give your answer correct to two decimal places.)


(d) Find the p-value. (Give your answer correct to four decimal places.)

Answer 1