A random sample of 31 sales charge showed a sample standard deviation of $50. A 90% confidence interval estimate of the population standard deviation is
A) 1715.101 to 4055.589.
B) 1596.458 to 4466.679.
C) 39.956 to 66.833.
D) 41.393 to 63.684.

Question

Quizplus · Accepted Answer

The formula for a confidence interval estimate of the population standard deviation is:
Confidence interval = (n-1)S^2 / χ^2(df, α/2) to (n-1)S^2 / χ^2(df, 1- α/2)
where S = sample standard deviation, n = sample size, df = degrees of freedom (df = n-1), and α is the level of significance.

Plugging in the given values, we get the confidence interval as:
(30*50^2 / χ^2(30, 0.05/2)) to (30*50^2 / χ^2(30, 1- 0.05/2))
= (48035.2 / 45.72) to (48035.2 / 17.71)
= 1050.2 to 2701.7

Therefore, the 90% confidence interval estimate of the population standard deviation is (1050.2, 2701.7). Option D is the only choice that falls within the range of this interval.

A Random Sample of 31 Sales Charge Showed a Sample