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 versus Ha: p ≠ .5 based on a random sample of 25 individuals. Let the test statistic X be the number in the sample who favor the first company and x represent the observed value of X.
a. Describe type I and II errors in the context of this problem situation.
b. Suppose that x = 6. Which values of X are at least as contradictory to H0 as this one?
c. What is the probability distribution of the test statistic X when H0 is true? Use it to compute the P-value when x = 6.
d. If H0 is to be rejected when P-value ≤ .044, compute the probability of a type II error when p = .4, again when p = .3, and also when p = .6 and p = .7.
e. Using the test procedure of (d), what would you conclude if 6 of the 25 queried favored company 1?