Question

A simple random sample of size 20 is drawn from a population that is known to be normally distributed. The sample​ variance, s squared​, is determined to be 12.4. Construct a​ 90% confidence interval for sigma squared. The lower bound is nothing. ​(Round to two decimal places as​ needed.) The upper bound is nothing. ​(Round to two decimal places as​ needed.)

Answer 1

df = n - 1 = 20 - 1 = 19

Chi-square critical values at 0.10 significance level with 19 df = L = 10.117 , U = 30.144

90% confidence interval for is

( n - 1) S² / U < < ( n - 1) S² / L

19 * 12.4 / 30.144 < < 19 * 12.4 / 10.117

7.82 < < 23.29

Lower bound = 7.82

Upper bound = 23.29