The 90% confidence interval estimate of a population standard deviation when a sample variance of 50 is obtained from a sample of 15 items is
A) 26.8 to 124.356.
B) 5.177 to 11.152.
C) 5.436 to 10.321.
D) 29.555 to 106.529.

Question

Quizplus · Accepted Answer

The formula to calculate the confidence interval of the population standard deviation is:
(√[ (n-1) s² / χ²_(α/2)(n-1)] , √[ (n-1) s² / χ²_(1-α/2)(n-1)])
where 
n = sample size, 
s² = sample variance, 
χ²_(α/2)(n-1) and χ²_(1-α/2)(n-1) are the chi-square values for the given level of confidence and degree of freedom (n-1).

Substituting the values in the formula, we get
(√[(15-1) 50 / χ²_(0.05/2)(14)], √[(15-1) 50 / χ²_(1-0.05/2)(14)])
= (√[14*50 / 6.572], √[14*50 / 26.119])
= (5.436, 10.321)

Therefore, the 90% confidence interval estimate of a population standard deviation is 5.436 to 10.321. Option C is the correct answer.

The 90% Confidence Interval Estimate of a Population Standard Deviation