A pharmaceutical company claims 90% success rate of a newly invented drug to treatarthritis pain. To examine the claim, a doctor administered the prescribed dose to 10arthritis patients. She observed Y, the number of participants for which the drug waseffective. A test is defined so as to reject Ho: p= 0.9 in favour of Ha: p< 0.9 bythe rejection region (y ≤k) where k is a positive integer. Note that p is the populationproportion of arthritis patients for which the drug was effective.(a) State what is meant by Type I and Type II errors in this context.(b) Find the value of a, the level of the test, if k= 6.(e) For a = 0.05, what should be the value of k if the rejection region of the test is{y

Write the given information.n = 10 Explain type I and type II error in this context.a)In hypothesis…

Answered: atients. She observed Y, the number of…

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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Question

A pharmaceutical company claims 90% success rate of a newly invented drug to treat
arthritis pain. To examine the claim, a doctor administered the prescribed dose to 10
arthritis patients. She observed Y, the number of participants for which the drug was
effective. A test is defined so as to reject Ho: p= 0.9 in favour of Ha: p< 0.9 by
the rejection region (y ≤k) where k is a positive integer. Note that p is the population
proportion of arthritis patients for which the drug was effective.
(a) State what is meant by Type I and Type II errors in this context.
(b) Find the value of a, the level of the test, if k= 6.
(e) For a = 0.05, what should be the value of k if the rejection region of the test is
{y <k}?

Expert Solution

Step 1: Explain type I and type II error in this context.

Write the given information.

$H subscript 0 space colon space p equals 0.90 H subscript A space colon space p less than 0.90$

n = 10

Explain type I and type II error in this context.

In hypothesis testing, type I error refers to rejecting the null hypothesis when it is true. In this context, it means that we decided to reject the null hypothesis(H₀: p = 0.9) and conclude that the success rate of the newly invented drug is less than 0.90 whereas actually null hypothesis(H₀: p = 0.9) is correct.

In the hypothesis testing, type II error refers to failing to reject the null hypothesis when it is false. In this context, it means that we decided to accept the null hypothesis(H₀: p = 0.9) and conclude that the success rate of the newly invented drug is 0.90 whereas actually null hypothesis(H₀: p = 0.9) is not correct.