Question

A random sample of rain collected over 12 rain-days yielded a sample standard deviation of s = .319. A normal probability plot suggests the data comes from a population that is normally distributed; moreover, it appears no outliers are present. A 90% confidence interval for the sample standard deviation is sought. With the knowledge of the chi-square values derived from the question directly above, determine the confidence interval for the population standard deviation. Choose the best answer. Group of answer choices ( .266 , .542 ) ( .057 , .245 ) ( .239 , .495 ) ( .231 , .463 )

Answer 1

Solution :

Given that

²_R = ²_/2,df = 19.675

²_L = ²_{1 - /2,df} = 4.575

The 90% confidence interval for is,

(n - 1)s² / ²_/2 < < (n - 1)s² / ²_{1 - /2}

  11 * 0.319 ² / 19.675 < < 11 * 0.319 ² / 4.575

0.239 < < 0.495

(0.239 , 0.495)