Question

If Katniss and Peeta want to find the proportion of people who believe in District 12 winning the hunger Games, how large of a sample size is required so that the margin of error is at most 2.5 percentage points with a 99% confidenve level? If there is not enough information given to answer the question, state the information you need.

Answer 1

Solution,

Given that,

= 0.12

1 - = 1 - 0.12 = 0.88

margin of error = E = 0.025

At 99% confidence level

= 1 - 99%  

= 1 - 0.99 =0.01

/2 = 0.005

Z/2 = Z0.005 = 2.576

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

= (2.576 / 0.025)2 * 0.12 * 0.88

= 1121.18

sample size = n = 1122