A sociologist develops a test designed to measure a person's attitudes about disabled people,and 16 randomly selected subjects are given the test.Their mean score is 71.2 with a standard deviation of 10.5.If the score is normally distributed,the 99% confidence interval for the mean score of all subjects would be _____.
A)[40.26,102.14]
B)[63.46,78.94]
C)[60.66,81.74]
D)[64.44,77.96]
E)[63.21,79.19]

Question

Quizplus · Accepted Answer

The 99% confidence interval for the mean can be calculated using 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 confidence level (for 99% confidence, $Z \approx 2.576$), $\sigma$ is the standard deviation, and $n$ is the sample size. Plugging in the given values: $71.2 \pm 2.576\frac{10.5}{\sqrt{16}}$, we get the interval $[63.46, 78.94]$.

A Sociologist Develops a Test Designed to Measure a Person's