Let T be a test statistic with a continuous and monotone probability distribution function Fo(t) := P(T≤t) under Ho. Then 1 - Fo(t) is the p-value of the test that rejects Ho for large values of t. (a) (b) Show that under Ho, the p-value 1 - Fo(T) is uniformly distributed in [0, 1]. Suppose now that you are not a fair scientist, so that you perform each experiment twice and you report just the highest p-value of each couple of measurements. Which is in this case the distribution of the reported p-values under Ho?
Let T be a test statistic with a continuous and monotone probability distribution function Fo(t) := P(T≤t) under Ho. Then 1 - Fo(t) is the p-value of the test that rejects Ho for large values of t. (a) (b) Show that under Ho, the p-value 1 - Fo(T) is uniformly distributed in [0, 1]. Suppose now that you are not a fair scientist, so that you perform each experiment twice and you report just the highest p-value of each couple of measurements. Which is in this case the distribution of the reported p-values under Ho?
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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Please provide some explanation with the taken steps, thank you in advance. (the question is in the attached image)
![Let T be a test statistic with
P(T≤t) under Ho. Then 1-
a continuous and monotone probability distribution function Fo(t) =
Fo(t) is the p-value of the test that rejects Ho for large values of t.
Show that under Ho, the p-value 1 - Fo(T) is uniformly distributed in [0, 1].
Suppose now that you are not a fair scientist, so that you perform each experiment
twice and you report just the highest p-value of each couple of measurements. Which is in this
case the distribution of the reported p-values under Ho?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8e237d3f-b8e6-4775-a6f9-5671b153aef2%2F3199f445-094c-4f16-a8ac-bfbefd7c00f6%2Fv04rt3_processed.png&w=3840&q=75)
Transcribed Image Text:Let T be a test statistic with
P(T≤t) under Ho. Then 1-
a continuous and monotone probability distribution function Fo(t) =
Fo(t) is the p-value of the test that rejects Ho for large values of t.
Show that under Ho, the p-value 1 - Fo(T) is uniformly distributed in [0, 1].
Suppose now that you are not a fair scientist, so that you perform each experiment
twice and you report just the highest p-value of each couple of measurements. Which is in this
case the distribution of the reported p-values under Ho?
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