Question

Find the critical values chi-squared Subscript 1 minus alpha divided by 2 and chi-squared Subscript alpha divided by 2 for a 98​% confidence level and a sample size of nequals20.

Answer 1

`\chi^2_(\alpha/2)=36.1909`

`\chi^2_(1-\alpha/2)=7.6327`

Explanation:

Given : The confidence level = 98 % = 0.98

Then, the significance level =
`\alpha=1-0.98=0.02`

Then,
`\alpha/2=(0.02)/(2)=0.01`

sample size : n= 20

Degree of freedom : df = n-1= 19

Now, using Chi-square distribution table , we have

`\chi^2_(\alpha/2)=\chi^2_(0.01)`

Check value for df = 19 and significance level = 0.01

`\chi^2_(\alpha/2)=36.1909`

Also,
`1-\alpha/2=1-0.01=0.99`

Check value for df = 19 and significance level = 0.99

`\chi^2_(1-\alpha/2)=\chi^2_(0.99)=7.6327`

Critical values :

`\chi^2_(\alpha/2)=36.1909`

`\chi^2_(1-\alpha/2)=7.6327`