Question

Considering the 5,800 enrollees in the College of Education, a researcher would like to make a study with 97.25% precision. How many samples must be taken?

Answer 1

We build 97.25% confidence interval for population mean or population proportion. This confidence interval covers population mean or population proportion with the probability 97.25%.

If we build 97.25% confidence interval for population mean:

Lower limit = $M-z_{1.375}\sigma_M$

Upper limit = $M+z_{1.375}\sigma_M$

Margin of error $ME=z_{1.375}\sigma_M$

$\sigma_M=\frac{\sigma}{\sqrt{N}}$

$M\text{ --- sample mean}\\ \sigma\text{ --- population standard deviation}\\ N\text{ --- sample size}\\ z_{1.375}\approx 0.0838\text{ --- the corresponding critical value}$

Then we have:

$N=\frac{z_{1.375}^2\sigma^2}{ME^2}$

If we build 97.25% confidence interval for population proportion:

$N=\frac{z_{1.375}^2p(1-p)}{ME^2}$

$p\text{ --- estimated proportion of the population which}\\ \text{has the attribute in question}.$