Chi-Squared confidence intervals - Confidence Intervals

Notes:

To estimate a population variance a Chi-Squared distribution is used,
• Chi-Squared: $X^2=\frac{(n-1)s^2}{\sigma ^2}$

$n$: sample size

$s$: sample standard deviation

$\sigma$: population standard deviation

$(n-1)$: is also called “degrees of freedom”
• Chi-Square table gives critical value area to the right

The Confidence interval for the variance is given by:
• $\frac{(n-1)s^2}{X_R^2}$ < $\sigma ^2$ < $\frac{(n-1)s^2}{X_L^2}$