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A study to test the null hypothesis H,:0=0, against H, :0 = 6, by using a critical region C={x:T(x)

A study to test the null hypothesis H,:0=0, against H, :0 = 6, by using a critical region C={x:T(x)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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A study to test the null hypothesis H,:0=0, against H, :0 = 6, by using a critical region C={x:T(x)<c}, where e is the critical value. Here, F,(z)=Pr (T <z;0) (a) denotes the sampling distribution of T(X) and t=T(x) denotes the reported sample statistic evaluated fot the data. %3D Demonstrate the size, a=F(c), power 1-ß = F, (c) _and p value, p = F, (t). (ii) Discover, if any of these three probabilities in Q2(a)(ii) depend solely on the null distribution and the critical value that the size of the test equal the p- (iii) value. By rearranging the inequality t < c, where c, = F"a(a), prove that t being in the critical region is equivalent to the p value being less than or cqual to the size of the test. (iv)
Transcribed Image Text:A study to test the null hypothesis H,:0=0, against H, :0 = 6, by using a critical region C={x:T(x)<c}, where e is the critical value. Here, F,(z)=Pr (T <z;0) (a) denotes the sampling distribution of T(X) and t=T(x) denotes the reported sample statistic evaluated fot the data. %3D Demonstrate the size, a=F(c), power 1-ß = F, (c) _and p value, p = F, (t). (ii) Discover, if any of these three probabilities in Q2(a)(ii) depend solely on the null distribution and the critical value that the size of the test equal the p- (iii) value. By rearranging the inequality t < c, where c, = F"a(a), prove that t being in the critical region is equivalent to the p value being less than or cqual to the size of the test. (iv)
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