A fire insurance company thought that the mean distance from

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 4.7 miles. It set its fire insurance rates accordingly. Members of the community set out to show that the mean distance was less than 4.7 miles. This, they thought, would convince the insurance company to lower its rates. They randomly indentified 67 homes and measured the distance to the nearest fire department from each. The resulting sample mean was 3.9. If = 1.9 miles, does the sample show sufficient evidence to support the community\'s claim at the = .05 level of significance?

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

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

Solution

a.) Z = (3.9 - 4.7)/(1.9/67) = - 3.45

b.) P value = 0.0003

Since pvalue is less than 0.05 we reject Ho