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Why can decreasing the probability of a type I error cause an increase in the probability of a type Il error? .....

Why can decreasing the probability of a type I error cause an increase in the probability of a type Il error? .....

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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Why can decreasing the probability of a type I error cause an increase in the probability of a type Il error? ..... Choose the correct answer below. O A. Decreasing a increases the probability of rejecting the null hypothesis. This decreases the probability of the complement, failing to reject the null hypothesis, which could increase the probability of failing to reject the alternative hypothesis when it is false, a type Il error. B. Decreasing a decreases the probability of failing to reject the null hypothesis. This increases the probability of the complement, rejecting the null hypothesis, which could increase the probability of rejecting the null hypothesis when it is true, a type Il error. O C. Decreasing a decreases the probability of rejecting the null hypothesis. This increases the probability of the complement, not rejecting the null hypothesis, which could increase the probability of failing to reject the null hypothesis when it is false, a type Il error. D. Decreasing a increases the probability of rejecting the null hypothesis, which increases the probability of rejecting the null hypothesis when it is true, a type II error.
Transcribed Image Text:Why can decreasing the probability of a type I error cause an increase in the probability of a type Il error? ..... Choose the correct answer below. O A. Decreasing a increases the probability of rejecting the null hypothesis. This decreases the probability of the complement, failing to reject the null hypothesis, which could increase the probability of failing to reject the alternative hypothesis when it is false, a type Il error. B. Decreasing a decreases the probability of failing to reject the null hypothesis. This increases the probability of the complement, rejecting the null hypothesis, which could increase the probability of rejecting the null hypothesis when it is true, a type Il error. O C. Decreasing a decreases the probability of rejecting the null hypothesis. This increases the probability of the complement, not rejecting the null hypothesis, which could increase the probability of failing to reject the null hypothesis when it is false, a type Il error. D. Decreasing a increases the probability of rejecting the null hypothesis, which increases the probability of rejecting the null hypothesis when it is true, a type II error.
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