Stat Question.pdf
Verify that {F}_{\alpha,n,m} = \frac{1}{{F}_{ \alpha,n,m } }
I am very frustrated with this verification. Attached is a PDF of the question because I don't know how to really work the formatting on this site. Please Help!
Stat Question.pdf
Verify that {F}_{\alpha,n,m} = \frac{1}{{F}_{ \alpha,n,m } }
I am very frustrated with this verification. Attached is a PDF of the question because I don't know how to really work the formatting on this site. Please Help!
An F distribution is equal in distribution to a ratio of chi-squares divided by their degrees of freedom. Hence, the distribution of 1/F is equal is also equal in distribution to a ratio of chi-squares divided by their degrees of freedom; you just end up switching the degrees of freedom. Use that fact to get the result.
First, use [tex] ... latex here ... [/tex] tags to post latex. Second, do you know what the value $\displaystyle F_{\alpha, n, m}$ indicates? I'll give you a hint: it's a certain percentile of the F distribution. With that in hand, think about what percentage of the F distribution alpha and 1-alpha are specifying, and see how they relate according to the provided equality. Your proof will derive from that understanding.