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. 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.