An inspector of flow metering devices used to administer fluid intravenously will perform a hypothesis test to determine whether the mean flow rate is different from the flow rate setting of 200 milliliters per hour. Based on prior information the standard deviation of the flow rate is assumed to be known and equal to 12 milliliters per hour. For each of the following sample sizes, and a fixed a = 0.05, find the probability of a type II error if the true mean is 205 milliliters per hour.
(a) n = 20
(b) n = 50
(c) n = 100
(d) Does the probability of a type II error increase or decrease as the sample size increases? Explain your answer.