Question

12) How many students do you need to estimate the mean GPA of Rancho Santiago Community College District students to within 1 with 98% confidence, if we assume that GPAs are between 1.0 and 4.07

Answer 1

Standard deviation by range rule of thumb

$=\frac{Range}{4}$

$=\frac{4-1}{4}$

=0.75

Therefore,           
              
Population standard deviation =0.75
Margin of error =E=0.1
Level of significance =   1-0.98=0.02
Z critical value is (by using Z table)=   2.326
Sample size formula is               
$n=\left [ \frac{Z*\sigma}{E} \right ]^{2}$
$=\left [ \frac{2.326*0.75}{0.1} \right ]^{2}$
=304.33  

$\approx 305$

n=305