Test the claim that the proportion of people who own cats is smaller than 70% at the 0.005 significance level. The null and alternative hypothesis would be: H0:p=0.7 H1:p≠0.7 H0:p≥0.7 H1:p<0.7 H0:μ≥0.7 H1:μ<0.7 H0:μ≤0.7 H1:μ>0.7 H0:p≤0.7 H1:p>0.7 H0:μ=0.7 H1:μ≠0.7 The test is: right-tailed two-tailed left-tailed Based on a sample of 500 people, 66% owned cats The p-value is: (to 2 decimals) Based on this we: Fail to reject the null hypothesis Reject the null hypothesis

Test the claim that the proportion of people who own cats is smaller than 70% at the 0.005 significance level. The null and alternative hypothesis would be: H0:p=0.7 H1:p≠0.7 H0:p≥0.7 H1:p<0.7 H0:μ≥0.7 H1:μ<0.7 H0:μ≤0.7 H1:μ>0.7 H0:p≤0.7 H1:p>0.7 H0:μ=0.7 H1:μ≠0.7 The test is: right-tailed two-tailed left-tailed Based on a sample of 500 people, 66% owned cats The p-value is: (to 2 decimals) Based on this we: Fail to reject the null hypothesis Reject the null hypothesis

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Description: Test the claim that the proportion of people who own cats is smaller than 70% at the 0.005 significance level.The null and alternative hypothesis would be: H0:p=0.7H1:p≠0.7H0:p≥0.7H1:p 0.7H0:p≤0.7H1:p>0.7H0:μ=0.7H1:μ≠0

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Concept explainers

2-Proportion Test

In a 2-proportion test, two separate proportions are measured at the same time, and their similarity is evaluated. It is also known as a 2-proportion z-test, and a comparison of two different proportions is done in this method.

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Test the claim that the proportion of people who own cats is smaller than 70% at the 0.005 significance level.

The null and alternative hypothesis would be:

H0:p=0.7
H1:p≠0.7

H0:p≥0.7
H1:p<0.7

H0:μ≥0.7
H1:μ<0.7

H0:μ≤0.7
H1:μ>0.7

H0:p≤0.7
H1:p>0.7

H0:μ=0.7
H1:μ≠0.7

The test is:

right-tailed

two-tailed

left-tailed

Based on a sample of 500 people, 66% owned cats

The p-value is: (to 2 decimals)

Based on this we:

Fail to reject the null hypothesis
Reject the null hypothesis

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Test the claim that the proportion of people who own cats is larger than 90% at the 0.005 significance level. The null and alternative hypothesis would be: Ho: ≤0.9 Ho:p ≤ 0.9 Ho: p=0.9 Ho: ≥ 0.9 Ho: = 0.9 Ho:p> 0.9 H₁: 0.9 H₁:p > 0.9 H₁:p # 0.9 H₁: < 0.9 H₁0.9 H₁ :p < 0.9 The test is: right-tailed left-tailed two-tailed Based on a sample of 200 people, 91% owned cats The p-value is: Based on this we: O Fail to reject the null hypothesis Reject the null hypothesis (to 2 decimals)
Test the claim that the proportion of people who own cats is smaller than 90% at the 0.025 significance level.The null and alternative hypothesis would be: H0:μ≥0.9H0:μ≥0.9 H1:μ<0.9H1:μ<0.9 H0:p≥0.9H0:p≥0.9H1:p<0.9H1:p<0.9 H0:p=0.9H0:p=0.9H1:p≠0.9H1:p≠0.9 H0:μ=0.9H0:μ=0.9H1:μ≠0.9H1:μ≠0.9 H0:p≤0.9H0:p≤0.9H1:p>0.9H1:p>0.9 H0:μ≤0.9H0:μ≤0.9H1:μ>0.9H1:μ>0.9 The test is: two-tailed right-tailed left-tailed Based on a sample of 200 people, 85% owned catsThe p-value is:  (to 2 decimals)Based on this we: Reject the null hypothesis Fail to reject the null hypothesis
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Test the claim that the proportion of people who own cats is significantly different than 40% at the 0.05 significance level.The null and alternative hypothesis would be: H0:p≥0.4H0:p≥0.4H1:p<0.4H1:p<0.4 H0:μ≤0.4H0:μ≤0.4H1:μ>0.4H1:μ>0.4 H0:μ≥0.4H0:μ≥0.4H1:μ<0.4H1:μ<0.4 H0:p≤0.4H0:p≤0.4H1:p>0.4H1:p>0.4 H0:p=0.4H0:p=0.4H1:p≠0.4H1:p≠0.4 H0:μ=0.4H0:μ=0.4H1:μ≠0.4H1:μ≠0.4 The test is: two-tailed left-tailed right-tailed Based on a sample of 700 people, 44% owned catsThe test statistic is: (to 2 decimals)The p-value is: (to 2 decimals)Based on this we: Reject the null hypothesis Fail to reject the null hypothesis
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Test the claim that the proportion of people who own cats is smaller than 50% at the 0.025 significance level.The null and alternative hypothesis would be: H0:p≤0.5H0:p≤0.5Ha:p>0.5Ha:p>0.5 H0:μ≥0.5H0:μ≥0.5Ha:μ<0.5Ha:μ<0.5 H0:p=0.5H0:p=0.5Ha:p≠0.5Ha:p≠0.5 H0:p≥0.5H0:p≥0.5Ha:p<0.5Ha:p<0.5 H0:μ=0.5H0:μ=0.5Ha:μ≠0.5Ha:μ≠0.5 H0:μ≤0.5H0:μ≤0.5Ha:μ>0.5Ha:μ>0.5 The test is: right-tailed two-tailed left-tailed Based on a sample of 700 people, 43% owned catsThe test statistic is:  (Round to 2 decimals)The p-value is:  (Round to 2 decimals)Based on this we: Reject the null hypothesis Do not reject the null hypothesis
Test the claim that the proportion of people who own cats is significantly different than 80% at the 0.1 significance level.The null and alternative hypothesis would be: H0:μ=0.8H0:μ=0.8H1:μ≠0.8H1:μ≠0.8 H0:p=0.8H0:p=0.8H1:p≠0.8H1:p≠0.8 H0:p≤0.8H0:p≤0.8H1:p>0.8H1:p>0.8 H0:p≥0.8H0:p≥0.8H1:p<0.8H1:p<0.8 H0:μ≤0.8H0:μ≤0.8H1:μ>0.8H1:μ>0.8 H0:μ≥0.8H0:μ≥0.8H1:μ<0.8H1:μ<0.8 The test is: right-tailed left-tailed two-tailed Based on a sample of 200 people, 87% owned catsThe p-value is:  (to 2 decimals)Based on this we: Reject the null hypothesis Fail to reject the null hypothesis
Test the claim that the proportion of men who own cats is smaller than 90% at the .05 significance level.The null and alternative hypothesis would be: H0:μ=0.9H0:μ=0.9H1:μ>0.9H1:μ>0.9 H0:p=0.9H0:p=0.9H1:p>0.9H1:p>0.9 H0:p=0.9H0:p=0.9H1:p≠0.9H1:p≠0.9 H0:μ=0.9H0:μ=0.9H1:μ≠0.9H1:μ≠0.9 H0:μ=0.9H0:μ=0.9H1:μ<0.9H1:μ<0.9 H0:p=0.9H0:p=0.9H1:p<0.9H1:p<0.9 The test is: right-tailed two-tailed left-tailed Based on a sample of 65 people, 87% owned catsThe test statistic is:  (to 2 decimals)The critical value is:  (to 2 decimals)Based on this we: Fail to reject the null hypothesis Reject the null hypothesis I dont understand this.