In a certain lake a limnologist wishes to estimate the proportion of lake trout with lamprey scars.
(a) How large of a random sample should be taken if the limnologist has no prior knowledge of the true proportion, but wants the bound to be within 0.04 with 90% confidence?
(b) How large should the sample be if the limnologist knows the true proportion does not exceed 0.20?
(c) If the limnologist caught 326 lake trout, and 47 had scars, calculate a 95% confidence interval for the true proportion of lake trout with lamprey scars.