F distributions - PowerPoint PPT Presentation

Chi-square and F Distributions

Chi-square and F Distributions. Children of the Normal. Questions. What is the chi-square distribution? How is it related to the Normal? How is the chi-square distribution related to the sampling distribution of the variance?

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705 views • 21 slides

Derivations of Student’s-T and the F Distributions

Derivations of Student’s-T and the F Distributions. Student’s-T Distribution (P. 1). Student’s T-Distribution (P. 2). Step 1: Fix V=v and write f ( z|v ) =f ( z ) (by independence) Step 2: Let T = h ( Z ) (and Z= h -1 ( T )) and obtain f ( t|v ) by method of transformations:

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289 views • 13 slides

Properties of t-distribution w/ n degrees of freedom (df): symmetric around zero (mean is zero)

What if the population standard deviation, s , is unknown ? We could estimate it by the sample standard deviation s which is the square root of the sample variance But what becomes of the standardized mean when s estimates s ?

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291 views • 4 slides

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