The article “An Evaluation of Football Helmets Under Impact Conditions” (Amer. J. Sports Medicine, 1984: 233–237) reports that when each football helmet in a random sample of 37 suspension-type helmets was subjected to a certain impact test, 24 showed damage. Let p denote the proportion of all helmets of this type that would show damage when tested in the prescribed manner.

a. Calculate a 99% CI for p.

b. What sample size would be required for the width of a 99%

CI to be at most .10, irrespective of pˆ?