A property and casualty insurance company (which provides firecoverage for dwellings) felt that the mean distance from a home tothe nearest fire department in rural Alabama was at least 10 miles.It set its fire insurance rates accordingly. Members of thecommunity set out to show that the mean distance was less than 10miles due to the increased number of volunteer fire departments.This, they felt, would convince the insurance company to lower itsrates. They randomly identify 64 homes and measure the distance tothe nearest fire department for each. The resulting sample mean was8.7 miles. If σ = 3.5 miles, does the sample show sufficientevidence to support the community’s claim? Use the four stepprocess for Hypothesis Testing.
Step 1 – State Hypothesis in contextof the problem.
Step 2 – Gather data, checkassumptions, and find rejection region using α.
Step 3 – Calculate the appropriatetest statistic and p-value.
Step 4 – State conclusion in contextof the problem.
