Question

A poll in Canada states that 67% of all respondents favor imposing the death penalty. The poll was considered accurate within 4.7 percentage points 95% of the time. How large was the sample size? Round up to the nearest whole number.

Answer 1

Solution,

Given that,

= 67% = 0.67

1 - = 1 - 0.67 = 0.33

margin of error = E = 4.7% = 0.047

At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025  = 1.96

sample size = n = (Z / 2 / E )2 * * (1 - )

= ( 1.96 / 0.047 )2 * 0.67 * 0.33

= 384.51

Sample size = n = 385