Question

A researcher wants to determine the proportion of pro-peace students at Rutgers University. He has no idea what the sample proportion will be. How large a sample is required to be 95% sure that the sample proportion is off by no more than 4% (E)

Answer 1

Answer:

The sample size is 601.

Explanation:

Given information:

Confidence interval = 95%

E = 4% = 0.04

From the z table it is clear that the z-value 95% confidence is 1.96.

A researcher wants to determine the proportion of pro-peace students at Rutgers University.

$p=0.5$

Formula for sample size is

$n=p(1-p)(\dfrac{z}{E})^2$

Substitute the given values in the above formula.

$n=0.5(1-0.5)(\dfrac{1.96}{0.04})^2$

$n=0.5(0.5)(49)^2$

$n=600.25$

Sample size can not be a decimal value. So, round the answer to the next whole number.

$n=601$

Therefore, the sample size is 601.