A sample of size 1 is taken from the geometric probability model, p X (k) (1 p) k1 p, k 1, 2, 3, , to test H 0 p 1 3 versus H 1 p 1 3 The null hypothesis is to be rejected if k 4 What is the probability that a Type II error will be committed when p 1 2 ...

A sample of size 1 is taken from the geometric probability model, p X (k) = (1

Question:

A sample of size 1 is taken from the geometric probability model, p_X(k) = (1 − p)^k−1 p, k = 1, 2, 3, . . . , to test H₀: p = 1/3 versus H₁: p > 1/3 . The null hypothesis is to be rejected if k ≥ 4. What is the probability that a Type II error will be committed when p = 1/2?