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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.

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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

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