Question

A simple random sample of 125 SAT scores has a mean of 1522. Assume that SAT scores have a population standard deviation of 335. Construct a 95% confidence interval estimate of the mean SAT score and then correctly interpret your interval.

Answer 1

Answer:

$1463.3\:$

Step-by-step explanation:

Since the population standard deviation $\sigma$, is known, we use the z confidence interval for the mean.

This is given by:

$\bar X-z_{\frac{\alpha}{2} }(\frac{\sigma}{\sqrt{n} } )\:$

For a 95% confidence interval we use $z=1.96$.

It was also given that: $n=125$, $\bar X=1522$ and $\sigma=335$

Let us substitute the values to get:

$1522-1.96(\frac{335}{\sqrt{125} } )\:$

$1463.3\:$

Interpretation:

We can say with 95% confidence that the interval between 1463.3 and 1580.7 SAT scores contains the population mean based on the sample 125 SAT scores.