A school-board administrator believes that the average number of days absent per year among students is less than 10 days. From past experience, he knows that the population standard deviation is 3 days. In testing to determine whether his belief is true, he could use one of the following plans:
i. n = 100, α = .01
ii. n = 75, α = .05
iii. n = 50, α = .10
Which plan has the lowest probability of a Type II error, given that the true population average is 9 days?