Question

You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately ˆ p (p-hat) = 77%`. You would like to be 95% confident that your esimate is within 2.5% of the true population proportion. How large of a sample size is required? n = Do not round until your final answer.

Answer 1

Solution :

Given that,

= 0.77

1 - = 1 - 0.77 = 0.23

margin of error = E = 2.5% = 0.025

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

Sample size = n = (Z_/2 / E)² * * (1 - )

= (1.96 / 0.025)² * 0.77 * 0.23

n = 1088.55

if we round this answer so answer will be 1089