Question

You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately p=0.69. You would like to be 95% confident that your esimate is within 2% of the true population proportion. How large of a sample size is required? Hint: Video [+]

Answer 1

Solution :

Given that,

$\hat p$= 0.69

1 - $\hat p$ = 1 - 0.69 = 0.31

margin of error = E = 2% = 0.02

At 95% confidence level the z is ,

$\alpha$ = 1 - 95% = 1 - 0.95 = 0.05

$\alpha$ / 2 = 0.05 / 2 = 0.025

Z_$\alpha$/2 = Z_0.025 = 1.96 ( Using z table ( see the 0.025 value in standard normal (z) table corresponding z value is 1.96 )

Sample size = n = (Z_$\alpha$/2 / E)² * $\hat p$ * (1 - $\hat p$ )

= (1.96 / 0.02)² * 0.69 * 0.31

= 2054.29

Sample size = 2054