According to data from the Environmental Protection Agency, the average daily water consumption for a household of four people in the United States is approximately at least 243 gallons. (Source: http://www

.catskillcenter.org/programs/csp/H20/Lesson3/house3

.htm) Suppose a state agency plans to test this claim using an alpha level equal to 0.05 and a random sample of 100 households with four people.

a. State the appropriate null and alternative hypotheses.

b. Calculate the probability of committing a Type II error if the true population mean is 230 gallons.

Assume that the population standard deviation is known to be 40 gallons.