Suppose you are interested in conducting the statistical test of H0: = 255 against Ha:

Suppose you are interested in conducting the statistical test of H0: μ = 255 against Ha: μ > 255, and you have decided to use the following decision rule: Reject H0 if the sample mean of a random sample of 81 items is more than 270. Assume that the standard deviation of the population is 63.

a. Express the decision rule in terms of z.

b. Find a, the probability of making a Type I error, by using this decision rule.