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1. Consider a population with proportion p. Let X be the number of successes in a random sample of size n, and X~ Bin(n, p). Consider the hypotheses, Ho: p = 0.15 versus H₁ : p=0.6. (a) A researcher decides to reject Ho if, in n = 7 trials, there are 4 or more successes (X > 4) and accept otherwise. Find the power of this test. (b) A researcher decides to reject Ho if, in n = 7 trials, there are 5 or more successes (X ≥ 5) and accept otherwise. Find the power of this test. (c) For each of the tests in Parts (a) and (b), find the probability of a type II error and compare them.

1. Consider a population with proportion p. Let X be the number of successes in a random sample of size n, and X~ Bin(n, p). Consider the hypotheses, Ho: p = 0.15 versus H₁ : p=0.6. (a) A researcher decides to reject Ho if, in n = 7 trials, there are 4 or more successes (X > 4) and accept otherwise. Find the power of this test. (b) A researcher decides to reject Ho if, in n = 7 trials, there are 5 or more successes (X ≥ 5) and accept otherwise. Find the power of this test. (c) For each of the tests in Parts (a) and (b), find the probability of a type II error and compare them.

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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Any help with this one will help. This is just a practice problem. Thanks

 

1. Consider a population with proportion p. Let X be the number of successes in a random sample of size n, and X~ Bin(n, p). Consider the hypotheses, Ho : p = 0.15 versus H₁ : p = 0.6. (a) A researcher decides to reject Hỏ if, in n = 7 trials, there are 4 or more successes (X > 4) and accept otherwise. Find the power of this test. (b) A researcher decides to reject Ho if, in n = 7 trials, there are 5 or more successes (X ≥ 5) and accept otherwise. Find the power of this test. (c) For each of the tests in Parts (a) and (b), find the probability of a type II error and compare them.
Transcribed Image Text:1. Consider a population with proportion p. Let X be the number of successes in a random sample of size n, and X~ Bin(n, p). Consider the hypotheses, Ho : p = 0.15 versus H₁ : p = 0.6. (a) A researcher decides to reject Hỏ if, in n = 7 trials, there are 4 or more successes (X > 4) and accept otherwise. Find the power of this test. (b) A researcher decides to reject Ho if, in n = 7 trials, there are 5 or more successes (X ≥ 5) and accept otherwise. Find the power of this test. (c) For each of the tests in Parts (a) and (b), find the probability of a type II error and compare them.
Expert Solution
Step 1: Given information:

1. 

The X is a random variable representing the number of successes in a random sample size n such that,

X tilde B left parenthesis n comma p right parenthesis

Sample size, n equals 7

The hypothesis is,

Null hypothesis, H subscript 0 colon p equals 0.15

Alternative hypothesis, H subscript 1 colon p equals 0.6


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