10.4 A fabric manufacturer believes that the propor- tion 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. 10.5 Repeat Exercise 10.4 but assume that 50 orders are selected and the critical region is defined to be x ≤ 24, where x is the number of orders in the sample that arrived late. Use the normal approximation.
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10.4 A fabric manufacturer believes that the propor-
tion 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.
10.5 Repeat Exercise 10.4 but assume that 50 orders
are selected and the critical region is defined to be
x ≤ 24, where x is the number of orders in the sample
that arrived late. Use the normal approximation.
Answer Exercise 10.5 only
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