Question

Determine the sample size needed to construct a 90​% confidence interval to estimate the average GPA for the student population at a college with a margin of error equal to 0.5. Assume the standard deviation of the GPA for the student population is 1.5.

Answer 1

Answer: 24

Step-by-step explanation:

The formula to calculate the sample size is given by :-

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

Given : Margin of error : $E=0.5$

The significance level : $\alpha=1-0.90=0.1$

Critical value : $z_{0.05}=\pm1.645$

Standard deviation : $\sigma=1.5$

Now, the required sample size will be :-

$n=(\frac{1.645\times1.5}{0.5})^2=24.354225\approx24$

Hence, the required sample size = 24