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 2 percentage points with 95​% confidence if ​(a) he uses a previous estimate of 36​%? ​(b) he does not use any prior​ estimates? ​(a) n= ​(Round up to the nearest​ integer.) ​(b) n= ​(Round up to the nearest​ integer.)

Answer 1

A researcher wishes to estimate the percentage of adults who support abolishing the penny.

size sample should be obtained if he wishes the estimate to be within 2 percentage points with 95​% confidence

​

(a) he uses a previous estimate of 36​%

Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)

Z a/2 at 0.05 is = 1.96

Sample Proportion = 0.36

ME = 0.02

n = ( 1.96 / 0.02 )^2 * 0.36*0.64

= 2212.76 ~ 2213

b.

he does not use any prior​ estimates

Assume

sample proportion =0.5%

Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)

Z a/2 at 0.05 is = 1.96

Sample Proportion = 0.5

ME = 0.02

n = ( 1.96 / 0.02 )^2 * 0.5*0.5

= 2401 ~ 2401