Chi square test for variance

• Assumptions

1. Data is normally distributed.

• 5-Step Hypothesis

Null and Alternative Hypothesis

• Ho: σ=σo
• Ha1: σ≠σo (Two tailed test)

Ha2: σ<σo (Left tailed test)

Ha3: σ>σo (Right tailed test)

Test Statistic

Critical value

• chisq(1-a/2,n-1), chisq(a/2,n-1) (Two tailed test)
• chisq(1-a,n-1) (Left tailed test)
• chisq(a,n-1) (Right tailed test)

P-value

• 2*(1-P(CHISQ≤|Chisq|) (Two tailed test)
• P(CHISQ≤Chisq) (Left tailed test)
• P(CHISQ≥Chisq) (Right tailed test)

Decision rule

• Reject Ho if chisq < chisq(1-a/2,n-1)  or chisq > chisq(a/2,n-1)  or p-value < alpha (two tailed test)
• Reject Ho if chisq < chisq(1-a,n-1)  or p-value < alpha (left tailed test)
• Reject Ho if chisq > chisq(a,n-1)  or p-value < alpha (right tailed test)

• Confidence Interval

100(1-alpha)% Confidence interval for the population variance is given by:

This implies I am 100(1-alpha)% confident that estimated population variance lies in the obtained interval.