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7. Let U~ N(0, 1) and V~ x²(v). If U and V are independent than has a student √VIV T-distribution with degrees of freedom. Using this result prove that the statistic T we used in the two-sample T test, has T-distribution under the null hypothesis. If the two sample sizes are m and n, what is the degrees of freedom of T?

7. Let U~ N(0, 1) and V~ x²(v). If U and V are independent than has a student √VIV T-distribution with degrees of freedom. Using this result prove that the statistic T we used in the two-sample T test, has T-distribution under the null hypothesis. If the two sample sizes are m and n, what is the degrees of freedom of T?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 31E
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U 7. Let U › N(0, 1) and V ~ x²(v). If U and V are independent than has a student √V/v T-distribution with degrees of freedom. Using this result prove that the statistic T we used in the two-sample T test, has T-distribution under the null hypothesis. If the two sample sizes are m and n, what is the degrees of freedom of T?
Transcribed Image Text:U 7. Let U › N(0, 1) and V ~ x²(v). If U and V are independent than has a student √V/v T-distribution with degrees of freedom. Using this result prove that the statistic T we used in the two-sample T test, has T-distribution under the null hypothesis. If the two sample sizes are m and n, what is the degrees of freedom of T?
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