Question

1) Find the critical values chi Subscript Upper R Superscript 2 and chi Subscript Upper L Superscript 2 for the given confidence level c and sample size n. c=0.95​, n=19

2) Use technology to construct the confidence intervals for the population variance sigma squared and the population standard deviation sigma. Assume the sample is taken from a normally distributed population. c=0.98 ,s^2=18.49 ,n=30

Answer 1

Solution :

1)

Given that,

n = 19

Degrees of freedom = df = n - 1 = 18

Critical values are :

²_L = ²_/2,df = 31.526

²_R = ²_{1 - /2,df} = 8.231

2)

Point estimate = s² = 18.49

n = 30

Degrees of freedom = df = n - 1 = 29

²_L = ²_/2,df = 49.588

²_R = ²_{1 - /2,df} = 12.256

The 98% confidence interval for ² is,

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

29 * 18.49 / 49.588 < ² < 29 * 49.588 / 12.256

10.81 < ² < 37.61

(10.81 , 37.61 )

The 98% confidence interval for is,

3.29 < < 6.13