Question

A researcher 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 5 percentage points with 90 ​% confidence if

​(a) he uses a previous estimate of 25 ​%? ​

(b) he does not use any prior​ estimates?

Answer 1

(a)

Margin of Error, E = 5% = 0.05

Z value for 90% confidence interval is 1.645

Proportion estimate, p = 0.25

Sample size, n =

= 202.9519   203 (Rounded to nearest integer)

(b)

If we do not have any prior​ estimates, we will assume p = 0.5, to calculate the conservative estimate of sample size.

Sample size, n =

= 270.6025   271 (Rounded to nearest integer)