Discussion
Two normal populations have variances \(\sigma_1^{2}\) = 10 and \(\sigma_2^{2}\) = 20. Two random samples of sizes 25 and 20, independently selected from these populations have variances of \(S_1^{2}\) = 8 and \(S_2^{2}\) = 15, respectively. What is the \(F_{(24, 19)}\) statistic ?
Answer: A
The F statistic is the ratio of the sample variances each divided by its population variance.
\[ F = \frac{S_1^2 / \sigma_1^2}{S_2^2 / \sigma_2^2} \]
\[ F = \frac{8/10}{15/20} \]
\[ F = \frac{0.8}{0.75} \approx 1.07 \]
The nearest value in the options is 1, option A, which is the keyed answer. The values 2, 2.81 and 3.6 are much larger.
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