A manufacturer of plumbing fixtures has developed a new type of washerless faucet. Let p = P(a randomly selected faucet of this type will develop a leak within 2 years under normal use). The manufacturer has decided to proceed with production unless it can be determined that p is too large; the borderline acceptable value of p is specified as .10. The manufacturer decides to subject n of these faucets to accelerated testing (approximating 2 years of normal use). With X = the number among the n faucets that leak before the test concludes, production will commence unless the observed X is too large. It is decided that if p = .10 , the probability of not proceeding should be at most .10, whereas if p = .30 the probability of proceeding should be at most .10. Can n = 10 be used? n = 20?n = 25 ? What is the appropriate rejection region for the chosen n, and what are the actual error probabilities when this region is used?
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