Question

Twenty-five juniors from a University volunteer to allow their Math GRE test scores to be used in a study. These 25 juniors had a mean Math GRE score of 450. Suppose we know that the standard deviation of the population of Math GRE scores for juniors at the University is σ = 100. Assuming the population of Math GRE scores for juniors at the University is approximately Normally distributed, a 90% confidence interval for the mean Math GRE score μ for the population of juniors computed from these data is

Answer 1

Let's start first by writing down the given:
σ = 100
sample mean = 450
sample size = 25

These information, plus the fact that we know that the population is approximately normally distributed, would tell us that we can use the normal distribution curve in analyzing the problem.

A confidence interval of the mean is just a range statistically estimated to contain the population mean. For a 90% confidence interval, we would look at the Z-table and see where 90% of the data falls. We'll notice that it will fall within 1.645 standard deviations of the mean.

Next, we look for the standard error of the mean. This will have a formula
$error= \frac{standard deviation of population}{ \sqrt{N} }$

The standard error would just therefore be equal to
$\frac{100}{ \sqrt{25} }= \frac{100}{5} =20$

Lastly, we just get the product of the standard error and 1.645 and add it to 450 for the maximum value and subtract it to 450 for the minimum value.
$450-20(1.645)=417.1$
$450+20(1.645)=482.9$

ANSWER: 417.1<μ<482.9