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.

Question

Quizplus · Accepted Answer

To construct the confidence interval, we need to use the formula:

CI = X̄ ± (Z* * s/√n)

Where: 
X̄ = sample mean (76.2) 
s = sample standard deviation (21.4) 
n = sample size (27) 
Z* = Z-value for the desired confidence level (95% in this case)

From the Z-table, the Z-value for 95% confidence level is 1.96.

Plugging in the values: 
CI = 76.2 ± (1.96 * 21.4/√27) 
CI = 76.2 ± 8.54

CI = (67.66, 84.74)

Therefore, the best choice is B, which is the closest to the calculated confidence interval.

A Sociologist Develops a Test to Measure Attitudes About Public