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 33 percentage points with 90​% confidence if ​

(a) he uses a previous estimate of 26​%?

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

a) n= ______ ​(Round up to the nearest​ integer.)

Answer 1

We are given the margin of error here as 33 percentage points that is 0.33

From standard normal tables, we have:
P( -1.645 < Z < 1.645) = 0.9

a) p = 0.26 is a prior estimate here.

The margin of error is computed as:

Therefore minimum 5 observations are required here.

b) As there is no prior estimate here, we use p = 0.5, to get a conservative sample size here.

Therefore minimum 7 observations are required here.