In Exercises 13–16, find the critical F-value for a two-tailed...

Question

In Exercises 13–16, find the critical F-value for a two-tailed test using the level of significance α and degrees of freedom d.f.N and d.f.D.

α=0.01,d.f.N=40,d.f.D=60

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. Determine the critical F value for a right tail test where alpha is equal to 0.05, numerator degrees of freedom 15, and denominator degrees of freedom 40. Awesome. So it appears for this particular problem we're asked to ultimately determine what the critical F value is for this right tail test given the information that is provided to us by the prom itself. So thinking about the conditions that are set to us by the prom itself, we're asked to determine what the critical F value is, and that is our final answer we're ultimately trying to solve for. So now that you know that we're trying to solve for the critical F value, let's read off our multiple choice answers to see what our final answer might be. A is 2.24, B is 2.10, C is 2.35, and D is 1.92. Awesome. So our first step that we need to take is we need to write down all of our known values. So we're told that alpha, the level of significance, is equal to 0.05. We're also told the degrees of freedom for the numerator, which we'll call DFN for short, and the degrees of freedom for the numerator is equal to 15, whereas the degrees of freedom for the denominator, which we'll call DFD. For short, so DFD, the degrees of freedom for the denominator is equal to 40. Awesome. So our second step now is we need to recall that we need to use a F distribution table, and there should be an F distribution table in your textbook or you could just quickly look up one online. And we need to use our F distribution table to help us find the critical value for alpha equals 0.05, 15 numerator degrees of freedom, and 40 denominator degrees of freedom. So let's make a note that we need to use our F distribution table, which we'll call it FDT for short, so we need to use our F distribution table. Fantastic. And our third step now is we need to take our we need to take our F distribution table, and we need to locate the intersection for 15 and 40 at alpha equals 0.05 in our table. Which will give us that F subscript 0.05.15.40 is approximately equal to, so once again using our table, we will find that our critical F value will be approximately equal to 1.92. All right, we did it. So that will mean our fourth and final step, we need to note that our critical F value without a doubt, will be equal to or rather approximately equal to 1.92. And that's it. That is our final answer. Hooray, we did it. And looking at our multiple choice answers, we will see that this corresponds to multiple choice answer letter D, which once again is 1.92. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

In Exercises 13–16, find the critical F-value for a two-tailed test using the level of significance α and degrees of freedom d.f.N and d.f.D.

α=0.01,d.f.N=40,d.f.D=60

Key Concepts

Critical F-value

Degrees of Freedom

Level of Significance (α)

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