A college admissions officer takes a simple random sample of 80 entering freshmen and computes their mean mathematics SAT score to be 469 . Assume the population standard deviation is $\sigma = 95$. Construct a $90 \%$ confidence interval for the mean mathematics SAT score for the enterin! freshmen class.
A) $( 374,564 )$
B) $( 467,471 )$
C) $( 452,486 )$
D) $( 455,483 )$

Question

Quizplus · Accepted Answer

To construct a 90% confidence interval for the mean, we use the formula: $\bar{x} \pm z \frac{\sigma}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $z$ is the z-score corresponding to the desired confidence level (for 90%, $z = 1.645$), $\sigma$ is the population standard deviation, and $n$ is the sample size. Plugging in the given values: $469 \pm 1.645 \times \frac{95}{\sqrt{80}}$, we calculate the margin of error and add/subtract it from the sample mean to find the confidence interval, which results in approximately $(452, 486)$.

A College Admissions Officer Takes a Simple Random Sample of 80