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 99​% confidence if

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

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

(a)n=

​(Round up to the nearest​ integer.)

Answer 1

Formula :

Where ,

P is previous estimate of population proportion, if P is not given than take it as 0.5

is z critical value for given confidence level.

E is margin of Error.

Given ,

Confidence level = 99% = 0.99

Significance level = 1- 0.99 = 0.01 , /2 = 0.005

So critical value is ,

= = 2.5857                  { Using Excel, = NORMSINV(0.005 ) = 2.5758 }

Margin of error = E = 5% = 0.05

a )
Previous estimate = P = 25% = 0.25

b )

Previous estimate is not known.

So take P = 0.5