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

Explanation:

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

`n=((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=((1.645*1.5)/(0.5))^2=24.354225\approx24`

Hence, the required sample size = 24