A fabric manufacturer believes that the proportion of orders for raw material arriving late is p = …

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 lt; 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.

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