The question asks whether the F-test statistic can ever be less than 1, given that $s_1^2$ represents the larger of two sample variances.

The F-test statistic is calculated as:

$F = \frac{s_1^2}{s_2^2},$

where $s_1^2 \geq s_2^2$ by definition (since $s_1^2$ is the larger variance). As a result:

1. The ratio $\frac{s_1^2}{s_2^2}$ will always be greater than or equal to 1.
2. Therefore, the F-test statistic can never be less than 1.

The correct answer is:

C. No, because the ratio $\frac{s_1^2}{s_2^2}$ will always be greater than 1.

Would you like more detailed reasoning on the F-test or further examples? Here are five related questions:

1. What is the purpose of an F-test in statistical analysis?
2. Can the F-test statistic ever be exactly equal to 1, and under what conditions?
3. How do degrees of freedom affect the F-test statistic?
4. What is the difference between a one-tailed and two-tailed F-test?
5. How is the F-test applied to test for equality of variances?

Tip: Always ensure the larger variance is in the numerator when calculating the F-test statistic to avoid incorrect interpretation.