Amanufacturer 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?