Question

The following sample of diameters was taken from 8 cans off the assembly line. Construct the 99% confidence interval for the population standard deviation for all cans that come off the assembly line. Round your answers to two decimal places. 9.7,9.8,9.4,9.0,8.8,9.1,9.2,8.8

Answer 1

Solution :
The statistic software output for this problem is:

Summary statistics:

Column	Variance
var2	0.145

²_L = ²_/2,df = 20.278

²_R = ²_{1 - /2,df} = 0.989

The 99% confidence interval for is,

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

  7 * 0.145 / 20.278 < < 7 * 0.145 / 0.989

0.22 < < 1.01

(0.22 , 1.01)