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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 P(X= k)| 0.006 1 2 3 5 6 7 8 9 10 0.040 0.121 0.215 0.251 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?

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 P(X= k)| 0.006 1 2 3 5 6 7 8 9 10 0.040 0.121 0.215 0.251 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?

Calculus For The Life Sciences
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 24CR
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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?
Transcribed Image Text: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

H0 : P=0.4

The test statistics is X=X1+....+X10

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