Use the structures of T and F given in Definitions 7.2 and

Chapter 7, Problem 33E

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QUESTION:

Use the structures of T and F given in Definitions 7.2 and 7.3, respectively, to argue that if T has a t distribution with ν df, then \(\mathrm{U}=\mathrm{T}^{2}\) has an F distribution with 1 numerator degree of freedom and ν denominator degrees of freedom.

Equation Transcription:

Text Transcription:

U=T^2

Questions & Answers

QUESTION:

Use the structures of T and F given in Definitions 7.2 and 7.3, respectively, to argue that if T has a t distribution with ν df, then \(\mathrm{U}=\mathrm{T}^{2}\) has an F distribution with 1 numerator degree of freedom and ν denominator degrees of freedom.

Equation Transcription:

Text Transcription:

U=T^2

ANSWER:

Step 1 of 2 

We have to use the structures of T and F given in Definitions 7.2 and 7.3, respectively, to argue that if T has a t distribution with  df, then  has an F distribution with 1 numerator degree of freedom and ? denominator degrees of freedom:

 

 

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