Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation σ.
Assume that the population has a normal distribution. Round the confidence interval limits to the same number of decimal places as the sample standard deviation.
-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 standard deviation, σ, of the scores of all subjects.
A) $16.6

Question

Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation σ.
Assume that the population has a normal distribution. Round the confidence interval limits to the same number of decimal places as the sample standard deviation.
-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 standard deviation, σ, of the scores of all subjects. 
A) $16.6 < \sigma < 28.6$
B) $17.2 < \sigma < 27.2$
C) $16.9 < \sigma < 29.3$
D) $17.5 < \sigma < 27.8$

Quizplus · Accepted Answer

We can use the chi-square distribution with n-1 degrees of freedom to construct the confidence interval. The formula for the confidence interval is:
[√((n-1)s^2)/χ^2(α/2,n-1), √((n-1)s^2)/χ^2(1-α/2,n-1)]
Substituting the given values, we get:
[√((27-1)(21.4)^2)/χ^2(0.025,26), √((27-1)(21.4)^2)/χ^2(0.975,26)]
Using a chi-square table or calculator, we find that χ^2(0.025,26) = 13.12 and χ^2(0.975,26) = 41.34. Substituting these values into the formula, we get:
[16.914, 29.267]
Rounding to one decimal place, we get:
[16.9, 29.3]
Therefore, the correct answer is C.

Use the Given Degree of Confidence and Sample Data to Find