Question

what is the critical f-value when the sample size for the numerator is six and the sample size for the denominator is four? use a two-tailed test and the 0.10 significance level. (round your answer to 2 decimal places.)

Answer 1

The critical f-value when the sample size for the numerator and the  denominator is given using a two-tailed test will be 0.12 and 14.88.

We have,

The sample size for the numerator = 6,

i.e.

Numerator degree of freedom = 6 - 1 = 5,

And,

The sample size for the denominator = 4,

i.e.

Denominator degree of freedom = 4 - 1 = 3

And,

We have to use a two-tailed test,

So,

The significance level = $\frac{0.10}{2}$ = 0.05

And,

Now,

The test follows the F-distribution with (5, 3) degrees of freedom,

Now,

Using the F-table at significance level 0.05 and check for given degrees of freedom,

We get,

Critical f-values : 0.12 and 14.88

Hence, we can say that the critical f-value when the sample size for the numerator and the  denominator is given using a two-tailed test will be 0.12 and 14.88.

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