A sample of 81 statistics students at a small college had a mean mathematics ACT score of 24 with a standard deviation of 8 . Find the $95 \%$ confidence interval. Round your answer to two decimal places.
A) $23.11

Question

A sample of 81 statistics students at a small college had a mean mathematics ACT score of 24 with a standard deviation of 8 . Find the $95 \%$ confidence interval. Round your answer to two decimal places.
A) $23.11 < \mu < 24.89$
B) $77.73 < \mu < 84.27$
C) $23.80 < \mu < 24.20$
D) $22.22 < \mu < 25.78$

Quizplus · Accepted Answer

The 95% confidence interval is calculated using the formula: $\bar{x} \pm z \times \frac{s}{\sqrt{n}}$, where $\bar{x} = 24$, $z = 1.96$ (for 95% confidence), $s = 8$, and $n = 81$. This gives $24 \pm 1.96 \times \frac{8}{\sqrt{81}} = 24 \pm 1.96 \times \frac{8}{9} = 24 \pm 1.74$, resulting in the interval $22.26 < \mu < 25.74$, which rounds to $22.22 < \mu < 25.78$.

A Sample of 81 Statistics Students at a Small College 95%95 \%95%

A Sample of 81 Statistics Students at a Small College $95 \%$