Reference no: EM13616905

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 0.10. 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=0.10, the probability of not proceeding should be at most 0.10, where as if p=0.30 the probability of proceeding should be at most 0.10. 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?