Use Table 2 in Appendix B and determine the critical region used in testing each of the following hypotheses. (Note: Since x is discrete, choose critical regions that do not exceed the value of  given.)

a. Ho : p  0.5 and Ha: p  0.5, where n  15 and

  0.05

b. Ho : p  0.5 and Ha: p  0.5, where n  14 and

  0.05

c. Ho : p  0.4 and Ha: p  0.4, where n  10 and

  0.10

d. Ho : p 

0.7 and Ha: p  0.7, where n  13 and

  0.01 9.101 You are testing the hypothesis p 

0.7 and have decided to reject this hypothesis if after 15 trials you observe 14 or more successes.

a. If the null hypothesis is true and you observe 13 successes, which of the following will you do? (1) Correctly fail to reject Ho. (2) Correctly reject Ho. (3) Commit a type I error. (4) Commit a type II error.

b. Find the significance level of your test.

c. If the true probability of success is 1/2 and you observe 13 successes, which of the following will you do? (1) Correctly fail to reject Ho. (2)

Correctly reject Ho. (3) Commit a type I error.

(4) Commit a type II error.

d. Calculate the p-value for your hypothesis test after 13 successes are observed.