A college admissions officer takes a simple random sample of 110 entering freshmen and computes their mean mathematics SAT score to be 465. Assume the population standard deviation is $\sigma = 92$ Construct a 90% confidence interval for the mean mathematics SAT score for the entering freshmen
Class.
A) (463, 467)
B) (451, 479)
C) (373, 557)
D) (446, 484)

Question

Quizplus · Accepted Answer

We can use the formula for a confidence interval for a population mean with known standard deviation:

$$\bar{x} \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$$

where $\bar{x}$ is the sample mean, $\sigma$ is the population standard deviation, $n$ is the sample size, and $z_{\alpha/2}$ is the critical value from the standard normal distribution corresponding to the desired confidence level (90% in this case).

Plugging in the values given, we get:

$$465 \pm 1.645 \frac{92}{\sqrt{110}} \approx 465 \pm 14.76$$

Simplifying, we get:

$$(450.24, 479.76)$$

Rounding to the nearest whole number, we get:

$$(451, 480)$$

Therefore, the best choice is B, which is the closest option to our interval.

A College Admissions Officer Takes a Simple Random Sample of 110