In Exercises 9–12, find the critical F-value for a right-taile...

Question

In Exercises 9–12, find the critical F-value for a right-tailed test using the level of significance α and degrees of freedom d.f.N and d.f.D.

α=0.05,d.f.N=20,d.f.D=25

Accepted Answer

Hello there. Today we're gonna solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. For a right-tailed ANOVA test, what is the critical F value when alpha equals 0.10, numerator degrees of freedom 8, and denominator degrees of freedom 18. Awesome. So it appears for this particular problem, we're ultimately trying to determine what is the critical F value given the conditions set to us by the prom itself. So with that in mind, now that we know we're ultimately trying to determine the value for the critical F value, let's read off our multiple choice answers to see what our final answer might be. So A is 2.23. B is 2.67, C is 2.04, and D is 2.44. Awesome. So first off, we need to write down all of our known variables. So we're told that the level of significance alpha is equal to 0.10. We're also told that the degrees of freedom for the numerator, which we'll call DFN, so the degrees of freedom for the numerator. is equal to 8, whereas the degrees of freedom for the denominator are equal to 18. Fantastic. So now that we know now that we've written down all of our known variables or all of our known values, our second step now is we need to use an F distribution table, which there should be an F distribution table in your textbook, and we need to use our F distribution table to help us find the critical value for when alpha is equal to 0.10. And when the numerator, so when there's an 8 numerator degrees of freedom and an 18 denominator degrees of freedom, So with that in mind, So let's make a note. So our second step is to use our F distribution table. So our F distribution table, so I'll call it FDT for short. So our second step is we need to look in our textbook or look up online in F distribution table. So now our third step. we need to locate the intersection for 8 and 18 at our level of significance of 0.10 in our table, which will give us that F subscript 0.10.8. 18 will be approximately equal to, so once again we'll find this value in our table, and when we do, we will find that it's approximately equal to 2.04. So that will mean that our fourth and final step is that our critical F value will be without a doubt, 2.04. And that will mean that our final answer corresponds to multiple choice answer letter C, which once again is 2.04. All right, we did it. We solve for this problem. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

In Exercises 9–12, find the critical F-value for a right-tailed test using the level of significance α and degrees of freedom d.f.N and d.f.D.

α=0.05,d.f.N=20,d.f.D=25

Key Concepts

Critical F-value

Degrees of Freedom

Significance Level (α)

Watch next