The watertreatment facility owners in Lake Havasu City, Arizona, recently proposed changes to all user fees. There is a treatment capacity fee, a connection fee, and a monthly minimum fee. All prices...

The watertreatment facility owners in Lake Havasu City, Arizona, recently proposed changes to all user fees. There is a treatment capacity fee, a connection fee, and a monthly minimum fee. All prices have been set assuming the mean monthly usage is 714 cubic feet per household. To check this claim, a random sample of 16 homes was obtained and the monthly usage for each home was recorded. The sample mean was 601.2 cubic feet. Assume the distribution of monthly water usage per household is normal with standard deviation 283 cubic feet.

a. Conduct a two-sided hypothesis test to determine whether there is any evidence the mean monthly water usage is different from 714 cubic feet. Use a = 0.05.

b. If your conclusion in part (a) is to not reject the null hypothesis, explain how this conclusion is possible even though the sample mean, 601.2, is so far away from the hypothesized mean, 714. If your conclusion in part (a) is to reject the null hypothesis, try checking your calculations one more time.