9. 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 rst company over the second. Consider testing H0: p  .5 versus Ha: p  .5 based on a random sample of 25 individuals. Let X denote the number in the sample who favor the rst company and x represent the observed value of X.

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

R1  {x: x 7 or x  18}, R2  {x: x 8}, R3  {x: x  17}

b. In the context of this problem situation, describe what 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?