A reseacher wishes to estimate the percentage of adults who

A reseacher wishes to estimate the percentage of adults who support abolishing the penny. What size sample should be obtained if he wishes the estimate to be within 2 percentage points with 95% confidence if.

a. he uses a previous estimate of 38%

b. he does not use any prior estimates.

Solution

95% confidence corresponds to z=1.96

E=z*sqrt(p*q/n) so n = p*q*(z/E)^2 and here E is given as 0.02.

a) p=0.38 so n = 0.38*0.62*(1.96/0.02)^2 = 2262.7 ~ 2263 Answer

b) p=q=0.5 so n = 0.5*0.5*(1.96/0.02)^2 = 2401 Answer