Say that we have a null hypothesis that X1,..., X16 that are Normally distributed with mean 0 and variance 1. Call the sample mean X. Consider the test where p-value = 20 (4 X) – 1 We will reject this if p-value < a. a) Show that the type I error rate of this test is a. b) Say that X1, .. What is the type II error rate of this test when a = X16 that are Normally distributed with mean 1 and variance 1. .... 0.05?

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question
Say that we have a null hypothesis that X1,..., X16 that are Normally distributed with
mean 0 and variance 1. Call the sample mean X. Consider the test where
p-value = 20 (4 X) -
24 (4|X) – 1
We will reject this if p-value < a.
a) Show that the type I error rate of this test is a.
b) Say that X1,..., X16 that are Normally distributed with mean 1 and variance 1.
What is the type II error rate of this test when a = 0.05?
•..
Transcribed Image Text:Say that we have a null hypothesis that X1,..., X16 that are Normally distributed with mean 0 and variance 1. Call the sample mean X. Consider the test where p-value = 20 (4 X) - 24 (4|X) – 1 We will reject this if p-value < a. a) Show that the type I error rate of this test is a. b) Say that X1,..., X16 that are Normally distributed with mean 1 and variance 1. What is the type II error rate of this test when a = 0.05? •..
Expert Solution
Step 1

Given that X1, . . ., X16 are normally distributed with mean 0 and variance 1.

p-value=2ϕ4X¯-1

steps

Step by step

Solved in 3 steps

Blurred answer
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman