For an F-distribution critical value, use the degrees of freedom n1-1, where n1 is the size of the sample with the larger variance. This reflects the degrees of freedom associated with the variance in the numerator of the F-statistic.
Option C is correct.
When looking up a critical value in an F distribution table, the number you use for the degrees of freedom of the numerator is n1-1, where n1 is the size of the sample with the larger s².
Here's why the other options are incorrect:
a. n2-1: This option refers to the degrees of freedom for the denominator, not the numerator. The F distribution requires two degrees of freedom, one for the numerator and one for the denominator. The denominator degrees of freedom depend on the size of the sample with the smaller variance (s²).
b. The larger of the two sample sizes minus one: This option is partially correct, but it doesn't specify which sample size to use. We need to use the degrees of freedom associated with the variance in the numerator of the F-statistic, which is the variance of the larger sample.
Therefore, based on the F-statistic's definition and the interpretation of degrees of freedom in hypothesis testing involving variances, the correct answer is c. n1-1, where n1 is the size of the sample with the larger s².
In conclusion, remember that the numerator degrees of freedom in the F distribution depend on the sample size associated with the larger variance, and you need to subtract 1 from that sample size to obtain the correct value.