"Finding a Critical F-Value for a Right-Tailed Test In Exercis...

Question

"Finding a Critical F-Value for a Right-Tailed Test In Exercises 5–8, 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=9, d.f.D=16"

Accepted Answer

Below 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 at alpha equals 0.10, with numerator degrees of freedom, DFN equals 7, and denominator degrees of freedom DFD equals 12. Awesome. So it appears for this particular problem we're ultimately trying to determine what the critical F value is for this right tail test given the specific data points provided to us by the prom itself. So given all the information that is provided to us by the problem itself, we're asked to determine what the critical F value is. So now that we know that we're trying to solve for this critical F value, let us read off our multiple choice answers to see what our final answer might be. A is 1.99, B is 2.85, C is 2.33. And D is 3.21. Awesome. So our first step that we need to take is we need to identify the level of significance, which we're told for this particular prompt. Alpha denotes this level of significance, and alpha in this case is equal to 0.10. And we're also told that the numerator degrees of freedom, which is denoted as DFN and the numerator degrees of freedom DFN is equal to 7, and the degrees of freedom for the denominator or the denominator degrees of freedom, DFD is is how it's denoted, is equal to 12 according to the prom itself. So our first step once again is we're trying to write down all of our known variables. Our second step now is we need to recall how to use an F distribution table or how to use a calculator in order to help us find the critical value for when the level of significance is equal to 0.10. And the numerator degrees of freedom is 7, and the denominator degrees of freedom is 12. So using those key pieces of information, we can use our F distribution table, which you should have one in your textbook or you quickly look one up online or we can use the calculator using these values. Our third and final steps, so our second step, let's make a note, we have to use our F distribution table, which we'll call FT for short. So we have to use our F distribution table and using our F distribution table or our calculator, which I'll just call C for short, our third step is we can officially determine what our critical F value is. So our critical F value is denoted as F subscript. 0.10.7.12. And our critical F value should be equal to 2.33, and this is our final answer. Hooray, we did it, and this corresponds to multiple choice answer letter C, which once again is 2.33, and that's it. That is our final answer. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

"Finding a Critical F-Value for a Right-Tailed Test In Exercises 5–8, 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=9, d.f.D=16"

Key Concepts

F-Distribution

Critical Value

Right-Tailed Test

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