Question

The National Center for Education would like to estimate the average student debt for the class of 2013 for the state of Ohio with a 95% con dence interval and a margin of error within plus or minus $2,000. Assuming the standard deviation for student debt in this state is $9,000, the required sample size is:

Answer 1

Answer:  78

Step-by-step explanation:

The formula use to find the sample size is given by :-

$n=(\dfrac{z_{\alpha/2}\ \sigma}{E})^2$

Given : Margin of error : $E=\pm\ 2,000$

Standard deviation : $\sigma=\ 9,000$

Significance level : $\alpha=1-0.95=0.05$

Critical value : $z_{\alpha/2}=1.96$

The formula use to find the sample size is given by :-

$n=(\dfrac{(1.96)\ (9000)}{2000})^2=77.7924\approx78$