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 versus 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?

R3 5 5x: x $ 176 R1 5 5x: x # 7 or x $ 186, R2 5 5x: x # 86, Ha H0: p 5 .5 : p 2 .5 Ha H : m . 1508 0: m 5 1508

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 , again when , and also for both and .

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