Q2 Problem 2: We are going to perform an exact binomial test for the population proportion.Let Ho: p = 0.4 and we get a sample of size 10. The test statistic is X = X₁ + ... + X10.Below is the table of probability mass function for Binomial(10, 0.4).k01234P(X= k) 0.006 0.040 0.121 0.215 0.25156789100.201 0.111 0.042 0.011 0.002 0.000(a) If H₁: p = 0.4, what is the critical region for the test statistic X so that the significancelevel a is closest to but does not exceed 0.1?(b) If H₁: p > 0.4, what is the critical region for the test statistic X so that the significancelevel a is closest to but does not exceed 0.1?

Answered: Problem 2: We are going to perform an…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Problem 2: We are going to perform an exact binomial test for the population proportion.
Let Ho: p = 0.4 and we get a sample of size 10. The test statistic is X = X₁ + ... + X10.
Below is the table of probability mass function for Binomial(10, 0.4).
k
0
1
2
3
4
P(X= k) 0.006 0.040 0.121 0.215 0.251
5
6
7
8
9
10
0.201 0.111 0.042 0.011 0.002 0.000
(a) If H₁: p = 0.4, what is the critical region for the test statistic X so that the significance
level a is closest to but does not exceed 0.1?
(b) If H₁: p > 0.4, what is the critical region for the test statistic X so that the significance
level a is closest to but does not exceed 0.1?

Expert Solution

Step 1

Introduction:

In statistics, a hypothesis test can be either a two-tailed test or a one-tailed test. A two-tailed test is used to test for a difference in two directions, while a one-tailed test is used to test for a difference in only one direction.

Tailed tests are used in hypothesis testing to determine whether a result is statistically significant or not. The choice between a one-tailed test and a two-tailed test depends on the research question and the directionality of the expected effect.

Given:

Sample size = 10

$H_{0} : P = 0.4$

The test statistics is $X = X_{1} + . . . . + X_{10}$