Suppose that a sequence of Bernoulli trials is to be carried out with an unknown probability θ of success on each trial, and the following hypotheses are to be tested:
H0: θ = 0.1,
H1: θ = 0.2.
Let X denote the number of trials required to obtain a success, and suppose that H0 is to be rejected if X ≤ 5. Determine the probabilities of errors of type I and type II.