"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=0.01, d.f.N=2, d.f.D=11"

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 with a value alpha equals 0.025 degrees of freedom value of DFN equals 4, and denominator degrees of freedom value of DFD equals 10. 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 specific values that are provided to us by the prom itself. So now that we know that we're ultimately trying to determine the critical F value for this right tail test, let us read off our multiple choice answers to see what our final answer might be. A is 5.96, B is 4.83, C is 5.25, and finally, D is 4.12. Awesome. So our first step that we need to take in order to solve for this particular prompt, we need to write down all of our known variables. So we're told that alpha, which is the level of significance, is equal to 0.025. We're also told the degrees of freedom, the numerator degrees of freedom, and the denominator degrees of freedom, which are DF. N and DFN. is equal to 4, and DFD, the denominator is equal to 10. So the degrees of freedom for the numerator is equal to 4, and the degrees of freedom for the denominator is equal to 10. Fantastic. So now, our second step, now that we've written down all of our known variables, we need to recall how to use a F distribution table to help us find the critical value for our level of significance of 0.025 and our degrees of freedom for the numerator and denominator. So when we take our given values, we're able to use, once again we're using our F distribution table, which you should have an F distribution table in your textbook or you quickly look one up online. But when you use the F distribution table, you should be able to determine that the critical F value will be F subscript 0.025. 4.10 will be equal to 4.83, and that is our final answer. Hooray, we did it, and this corresponds to multiple choice answer letter B, which once again is 4.83. 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=0.01, d.f.N=2, d.f.D=11"

Key Concepts

F-Distribution

Critical Value

Right-Tailed Test

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