Explanation

The F-test is the most appropriate statistical test for comparing the variances of two normally distributed populations. Here's why:

Key Points:

1. F-test Purpose: The F-test is specifically designed to compare the variances of two independent samples from normally distributed populations.
2. Test Statistic: The F-statistic is calculated as the ratio of the two sample variances: $F = \frac{s_1^2}{s_2^2}$ where $s_1^2$ and $s_2^2$ are the sample variances.
3. Assumptions: The F-test assumes that both populations are normally distributed and that the samples are independent.

Why Other Options Are Incorrect:

• B. Chi-square test: This test is used for testing variance of a single population against a hypothesized value, not for comparing variances of two populations.
• C. Paired comparisons test: This test (like paired t-test) is used for comparing means of two related samples, not variances.

Application in CFA Context:

In financial analysis, the F-test is commonly used to:

• Test for equal variances in regression analysis (homoscedasticity)
• Compare risk measures between two investment portfolios
• Analyze differences in volatility between two asset classes

Important Note:**

When using the F-test, it's conventional to place the larger sample variance in the numerator to ensure the F-statistic is ≥ 1. This simplifies the interpretation of the test results.