Question

Thirty-three college freshmen were randomly selected for an on-campus survey at their university. The participants' mean GPA was 2.5, and the standard deviation was 0.5. What is the margin of error, assuming a 95% confidence level

Answer 1

The margin of error is ±0.1706

What is the margin of error?

The margin of error is a statistical solution for the amount of random sampling error in the survey results.

What is 95% of a confidence level?

The 95% confidence interval means from 100 different samples computing a 95% of confidence for each sample. From this, we get the approximate value 95 of the 100 confidence intervals will contain the true mean value.

We have a sample size of n=33

The critical value of the significance level is $\alpha =0.05\\z_{\frac{\alpha }{2} }=1.96$

Then our sample mean will be 2.5

then the standard deviation is 0.5

from this, we can assume that this is a normal distribution.

then our margin of error will be

$E=$±$z_{\frac{\alpha }{2} }\frac{deviation}{\sqrt{n} }$

⇒$E=$±$(1.96)\frac{0.5}{\sqrt{33} }$

≅±0.1706 is the margin of error.

Learn more about the margin of error here:

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