A sociologist develops a test to measure attitudes about public transportation, and 27 randomly selected subjects are given the test.Their mean score is 76.2 and their standard deviation is 21.4.Construct the 95% confidence interval for the mean score of all such subjects ________________________ .
Please fix alignment
A)(64.2, 88.2)
B)(67.7, 84.7)
C)(64.2, 83.2)
D)(69.2, 83.2)
E)(74.6, 77.8)

Question

Quizplus · Accepted Answer

To construct a 95% confidence interval for the mean score of all such subjects, we use the formula for the confidence interval for a mean, which is $\bar{x} \pm t_{\alpha/2} \cdot \frac{s}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $s$ is the sample standard deviation, $n$ is the sample size, and $t_{\alpha/2}$ is the t-score corresponding to the desired confidence level and degrees of freedom (df = n - 1). Given $\bar{x} = 76.2$, $s = 21.4$, and $n = 27$, and knowing that the t-score for a 95% confidence interval with 26 degrees of freedom is approximately 2.056 (this value might slightly vary depending on the source, but it's close to 2 for large sample sizes), we calculate the margin of error and then the confidence interval. The correct calculation leads to the interval (67.7, 84.7), which matches choice B.

A Sociologist Develops a Test to Measure Attitudes About Public