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:

Respuesta :

Answer:  78

Step-by-step explanation:

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

[tex]n=(\dfrac{z_{\alpha/2}\ \sigma}{E})^2[/tex]

Given : Margin of error : [tex]E=\pm\$2,000[/tex]

Standard deviation : [tex]\sigma=\$9,000[/tex]

Significance level : [tex]\alpha=1-0.95=0.05[/tex]

Critical value : [tex]z_{\alpha/2}=1.96[/tex]

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

[tex]n=(\dfrac{(1.96)\ (9000)}{2000})^2=77.7924\approx78[/tex]