Two different companies have applied to provide cable television service in a certain region. Let p denote the proportion of all potential subscribers who favor the first company over the second. Consider testing H0 : p = .5 vs HA : P ≠ .5 based on a random sample of 25 individuals. Let X denote the number in the sample who favor the first company and x represent the observed value of X.

i. Which of the following rejection regions is most appropriate and why?

R1 = {x : x 18}

R2 = {x : x R3 = {x : x>17}

ii. In the context of this problem situation, describe what type I and type II errors are.

iii. Compute the probability of a type II error for the selected region in part (a) when p = .3, p = .4, p = .5, and p = .6.