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 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. O B. 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. OC. 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. O D. 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 II error.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 8CR
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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 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 II error.
B. 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 II error.
Decreasing & 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.
C.
O D.
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 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 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 II error. B. 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 II error. Decreasing & 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. C. O D. 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 II error.
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