To construct the confidence interval for the population variance $\sigma^2$, we can use the chi-square distribution. The formula for the confidence interval for the population variance is given by:

$\left( \frac{(n - 1) \cdot s^2}{\chi^2_{\alpha/2}}, \frac{(n - 1) \cdot s^2}{\chi^2_{1 - \alpha/2}} \right)$

Where:

• $n$ is the sample size (22 in this case),
• $s^2$ is the sample variance (the square of the sample standard deviation),
• $\alpha$ is the level of significance (for a 95% confidence interval, $\alpha = 0.05$),
• $\chi^2_{\alpha/2}$ and $\chi^2_{1 - \alpha/2}$ are the critical values from the chi-square distribution for $n - 1$ degrees of freedom.

Step 1: Find the sample variance

The