The binomial random variable, x, may be used as the test statistic when testing hypotheses about the binomial parameter, p.When n is small (say, 15 or less), Table 2 in Appendix B provides the probabilities for each value of x separately, thereby making it unnecessary to estimate probabilities of the discrete binomial random variable with the continuous standard normal variable z. Use Table 2 to determine the value of a for each of the following:
a. Ho: p = 0.5 and Ha: p_0.5 where n = 15 and the critical region is x = 12, 13, 14, 15
b. Ho: p = 0.3 and Ha: p < 0.3 where n = 12 and the critical region is x = 0, 1
c. Ho: p = 0.6 and Ha: p ≠ 0.6, where n = 10 and the critical region is x = 0 1, 2, 3, 9, 10
d. Ho: p = 0.5 and Ha: p > 0.05, where n = 14 and the critical region is x =4 5, 6, 7, . . . , 14