A sociologist develops a test to measure attitudes towards public transportation, and 47 randomly selected subjects are given the test. Their mean score is 76.2 and their standard deviation is 21.4.
Construct an approximate 95% confidence interval for the mean score of all such subjects.
A) $76.2 \pm 0.91$
B) $76.2 \pm 6.87$
C) $76.2 \pm 6.24$
D) $76.2 \pm 3.12$

Question

A sociologist develops a test to measure attitudes towards public transportation, and 47 randomly selected subjects are given the test. Their mean score is 76.2 and their standard deviation is 21.4.
Construct an approximate 95% confidence interval for the mean score of all such subjects. 
A) $76.2 \pm 0.91$
B) $76.2 \pm 6.87$
C) $76.2 \pm 6.24$
D) $76.2 \pm 3.12$

Quizplus · Accepted Answer

The 95% confidence interval is calculated using the formula: mean ± (critical value) * (standard deviation/√n). Here, the critical value for 95% confidence is approximately 1.96, and the sample size is 47. Thus, the margin of error is 1.96 * (21.4/√47) ≈ 6.24.

A Sociologist Develops a Test to Measure Attitudes Towards Public 76.2±0.9176.2 \pm 0.9176.2±0.91

A Sociologist Develops a Test to Measure Attitudes Towards Public $76.2 \pm 0.91$