The following is a Minitab printout of the binomial pdf p_X(k) = (9/k) (0.6)^k(0.4)^9−k, k = 0, 1, . . . , 9. Suppose H₀: p = 0.6 is to be tested against H₁: p > 0.6 and we wish the level of significance to be exactly 0.05. Use Theorem 2.4.1 to combine two different critical regions into a single randomized decision rule for which α = 0.05.

MTB > pdf;

SUBC > binomial 9 0.6.

Probability Density Function

Binomial with n = 9 and p = 0.6

x                                  P(X = x)

0…………………..    0.000262

1…………………..    0.003539

2…………………..    0.021234

3…………………..    0.074318

4…………………..    0.167215

5…………………..    0.250823

6…………………..    0.250823

7…………………..    0.161243

8…………………..    0.060466

9…………………..    0.010078