Each day, a fast-food chain tests that the average weight of its "two-pounders" is at least 32 ounces. The alternative hypothesis is that the average weight is less than 32 ounces, indicating that new processing procedures are needed. The weights of two-pounders can be assumed to be normally distributed, with a standard deviation of 3 ounces. The decision rule adopted is to reject the null hypothesis if the sample mean weight is less than 30.8 ounces.
a. If random samples of n = 36 two-pounders are selected, what is the probability of a Type I error, using this decision rule?
b. If random samples of n = 9 two-pounders are selected, what is the probability of a Type I error, using this decision rule? Explain why your answer differs from that in part a.
c. Suppose that the true mean weight is 31 ounces. If random samples of 36 two-pounders are selected, what is the probability of a Type II error, using this decision rule?