Financial Risk Manager Part 1

The chi-squared test is the most common hypothesis test for the variance of a normally distributed population. This is because when testing the variance of a normal distribution, the test statistic follows a chi-squared distribution. The chi-squared test statistic is calculated as:

$\chi^2 = \frac{(n-1)s^2}{\sigma_0^2}$

where:

• $n$ is the sample size
• $s^2$ is the sample variance
• $\sigma_0^2$ is the hypothesized population variance

This test statistic follows a chi-squared distribution with $(n-1)$ degrees of freedom under the null hypothesis.

Why other options are incorrect:

• F-test: Used for comparing variances of two normally distributed populations, not testing a single variance against a hypothesized value.
• Z-test: Used for testing means when population variance is known, not for testing variances.
• t-test: Used for testing means when population variance is unknown, not for testing variances.