Question

2. 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 90​% confidence if ​

(a) he uses a previous estimate of 22​%?

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

3. In a​ poll, 37​% of the people polled answered yes to the question​ "Are you in favor of the death penalty for a person convicted of​ murder?" The margin of error in the poll was 3%, and the estimate was made with 96​% confidence. At least how many people were​ surveyed?

Answer 1

2)

Sample size = Z2/2 * p ( 1 - p) / E2

a)

n = 1.64492 * 0.22 ( 1 - 0.22) / 0.022

= 1160.7

n = 1161 (Rounded up to nearest integer)

b)

When prior estimate for proportion is not specified then p = 0.50

n = 1.64492 * 0.50 ( 1 - 0.50) / 0.022

= 1691.06

n = 1692 (Rounded up to nearest integer)

3)

Sample size = Z2/2 * p ( 1 - p) / E2

n = 2.05372 * 0.37 ( 1 - 0.37) / 0.032

= 1192.38

n = 1193 (Rounded up to nearest integer)