Question

What is the critical f-value when the sample size for the numerator is four and the sample size for the denominator is seven? use a one-tailed test and the 0.01 significance level.

Answer 1

Assuming that we are performing a two-tailed test, the significance level is α = 0.1 would be dispersed in the distribution's tails with α/2  = 0.05.

And we must consider two critical values that add up to 0.05 of a area on every tail of a F distribution with a 10 degree angle.

$\begin{aligned}&F_{\alpha / 2}=0.311 \\&F_{1-\alpha / 2}=4.06\end{aligned}$

What is critical f-value?

An F statistic is one that is ascertained through an ANOVA test. It helps determine the relevance of the variable groups.

Now, according to the question;

We understand that sample size for numerator is 11 and also the sample size for denominator is 7. So, for each case, we can calculate a degrees of freedom as follows:

$\begin{aligned}&d f_{\text {num }}=11-1=10 \\&d f_{d e n}=7-1=6\end{aligned}$

In this case, the F distribution could have 10 degrees of freedom with in numerator as well as 6 degrees of freedom in the denominator.

Assuming we are conducting a two-tailed test, the significance level of α = 0.1 will be distributed in the tails of the distribution with α/2  = 0.05.

Now, locate two critical values that collect 0.05 of a area on every tail of F distribution to 10 degrees of freedom again for numerator and 6 degrees of freedom for the denominator and we obtained using a table or excel;

$\begin{aligned}&F_{\alpha / 2}=0.311 \\&F_{1-\alpha / 2}=4.06\end{aligned}$

Therefore, the critical f-value for the two-tailed experiment is found.

To know more about the critical f-value, here

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