# Scott wants to find a 95% confidence interval for the average GPA for Allegany College of Maryland students. He gets the records for 89 student. The results were roughly bell-shaped with a mean of 2.3 and standard deviation of 0.7. Construct a 95% confidence interval in the form: Estimate pm margin of error.

Question
Confidence intervals
Scott wants to find a $$95\%$$ confidence interval for the average GPA for Allegany College of Maryland students. He gets the records for 89 student. The results were roughly bell-shaped with a mean of 2.3 and standard deviation of 0.7. Construct a $$95\%$$ confidence interval in the form: Estimate $$\pm$$ margin of error.

2021-01-16
Step 1
Confidence interval are of utmost importance in statistics. It forms an integral part of hypothesis testing.
Step 2
The estimate is the mean $$\displaystyle={2.4}$$
The margin of error is $$\displaystyle\frac{\sigma}{\sqrt{{n}}^{\tau}}{0.025}=\frac{0.7}{\sqrt{{89}}}{\left({1.96}\right)}={0.4986}$$
n is the sample size, $$\displaystyle\sigma$$ is the standard deviation.

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