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The number of defective widgets produced by a machine in a batch of 40 can be modeled by a binomial distribution. The manufacturer claims the defect rate is 5%. An inspector, Lee, believes the true defect rate is higher and decides to conduct a test:
He inspects one batch of 40 widgets.
If he finds 3 or more defectives, he will reject the manufacturer’s claim.
State a suitable null and alternative hypothesis for Lee’s test.
Find the probability of a Type I error.
Suppose the true defect rate is actually 8%.
Find the probability of a Type II error.
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