1)

l. [16 pts.) Suppose the time that it takes for a certain infection to be cured is Normally distributed with mean (in days} ,5: and standard deviation 0' = 1 day. The drug manufacturer advertises that it works in 5 days1 on average1 but measurements on a random sample of l patients gave a mean infection time of 3': = 5.2 days. Is this evidence that the mean time to be cured is actually more than advertised? (a) To answer this, test the following hypotheses at signicance level a= ill. H:p=51Ha:p}5 (b) In the context of this example, describe in words the meaning of type I error. What is the consequence of type I error and is it serious