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

Answer:

$\chi^2_{\alpha/2}=36.1909$

$\chi^2_{1-\alpha/2}=7.6327$

Step-by-step explanation:

Given : The confidence level = 98 % = 0.98

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

Then,  $\alpha/2=\dfrac{0.02}{2}=0.01$

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 :

$\chi^2_{\alpha/2}=36.1909$

$\chi^2_{1-\alpha/2}=7.6327$