What is the test statistic for testing the equality of two variances?

What is the test statistic for testing the equality of two variances?

• A. Chi-square statistic
• B. F = s1^2 / s2^2
• C. t statistic
• D. Z statistic

Answer: (B)

The test uses the ratio of the two sample variances. When data come from normal populations, the ratio s1^2 / s2^2 follows an F distribution with degrees of freedom n1−1 and n2−1 under the null hypothesis that the population variances are equal. So you compute F = s1^2 / s2^2 and compare it to the F distribution to decide whether to reject equality of variances. The other statistics are used for different problems: the chi-square statistic targets a single variance against a known value, while the t and z statistics are used for testing means (not variances).

The test uses the ratio of the two sample variances. When data come from normal populations, the ratio s1^2 / s2^2 follows an F distribution with degrees of freedom n1−1 and n2−1 under the null hypothesis that the population variances are equal. So you compute F = s1^2 / s2^2 and compare it to the F distribution to decide whether to reject equality of variances. The other statistics are used for different problems: the chi-square statistic targets a single variance against a known value, while the t and z statistics are used for testing means (not variances).