A 95% confidence interval is (54.5, 57.5) based on a sample size of 25. What is the sample standard deviation?
A) 3.826
B) 19.132
C) 8.973
D) 11.646

Question

Quizplus · Accepted Answer

The confidence interval is calculated as $ \bar{x} \pm Z \frac{s}{\sqrt{n}} $, where $ \bar{x} $ is the sample mean, $ Z $ is the Z-score corresponding to the confidence level (for 95%, $ Z \approx 1.96 $), $ s $ is the sample standard deviation, and $ n $ is the sample size. The width of the confidence interval is $ 2 \times Z \frac{s}{\sqrt{n}} $. From the given interval (54.5, 57.5), the mean $ \bar{x} = 56 $ and the margin of error $ Z \frac{s}{\sqrt{n}} = 1.5 $. Rearranging for $ s $, $ s = \frac{1.5 \times \sqrt{n}}{Z} $. Substituting $ n = 25 $ and $ Z = 1.96 $, $ s = \frac{1.5 \times \sqrt{25}}{1.96} = \frac{1.5 \times 5}{1.96} = 3.826 $.

A 95% Confidence Interval Is (54