In the article" Explaining an Unusual Allergy",appearing on the Everyday Health Network, Dr.A.Feldweg explained that allergy to sulfites is usually seen in paints with asthma. The typical reaction is a sudden increase in asthma after eating a food containing sulfites. Studies are performed to estimate the percentage of the nation's 10 million asthmatics who are allergic to sulfites. In one survey, 38 of 500 normally selected U.S. asthmatics were found to be allergic to sulfites.
(a) Make a point estimate for the proportion of all U.S. asthmatics who are allergic to sulfites. Find the margin or error for this estimate at 99% confidence.
(b) Find the 99% confidence interval estimate for the proportion in (a).
(c) Using 99 %, suppose we wanted to reduce the margin of error to 2%. What is the required sample size, assuming we have no estimate of the sample proportion available?