Two different companies have applied to provide cable television service in a certain re...

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 = .5versus H_a: 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.

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

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

c. What is the probability distribution of the test statistic X when H₀ is true? Use it to compute the probability of a type I error.

d. Compute the probability of a type II error for the selected region when p = .3 again when p = .4 and also for both p = .6 and p = .7

e. Using the selected region, what would you conclude if 6 of the 25 queried favored company 1?