A fabric manufacturer believes that the proportion of orders for raw material arriving late is p = 0.6. If a random sample of 10 orders shows that 3 or fewer arrived late, the hypothesis that p = 0.6 should be rejected in favor of the alternative p < 0.6. Use the binomial distribution.

(a) Find the probability of committing a type I error if the true proportion is p = 0.6.

(b) Find the probability of committing a type II error for the alternatives p = 0.3, p — 0.4, and p = 0.5.