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

Explanation:

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

`n=((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=(((1.96)\ (9000))/(2000))^2=77.7924\approx78`