The 90% confidence interval estimate for a population standard deviation when a sample variance of 50 is obtained from a sample of 15 items is
A)4.18 to 15.07
B)5.18 to 11.15
C)5.44 to 10.32
D)29.55 to 106.53

Question

Quizplus · Accepted Answer

To calculate the confidence interval for population standard deviation with known sample variance, we use the formula:
CI = [(n-1) * s^2 / X^2(α/2), (n-1) * s^2 / X^2(1-α/2)]
where n is the sample size, s^2 is the sample variance, X^2(α/2) and X^2(1-α/2) are the chi-squared values corresponding to the upper and lower percentages of the confidence level, respectively.
In this case, n = 15, s^2 = 50, and we want a 90% confidence interval.
Using a chi-squared distribution table or calculator, we find that X^2(0.05) = 23.68 and X^2(0.95) = 6.26 (since we want a two-tailed test).
Plugging in the values, we get:
CI = [(15-1) * 50 / 23.68, (15-1) * 50 / 6.26]
CI = [4.18, 15.07]
Therefore, the 90% confidence interval estimate for a population standard deviation is 5.44 to 10.32 (Option C).

The 90% Confidence Interval Estimate for a Population Standard Deviation