**Testing the Claim About Cat Ownership***Objective*: Test the claim that the proportion of people who own cats is smaller than 10% at the 0.025 significance level.**Hypotheses**:- Null Hypothesis \( (H_0) \): \( p \leq 0.1 \)- Alternative Hypothesis \( (H_1) \): \( p > 0.1 \)**Type of Test**:- The test is: Left-tailed**Sample Data**:- Based on a sample of 600 people, 5% owned cats.**P-value**:- The p-value is: [Blank space] (to 2 decimals)**Conclusion**:- Based on this we: - \( \circ \) Reject the null hypothesis - \( \circ \) Fail to reject the null hypothesis*Note*: The specific hypothesis notation offers multiple ways to express population parameters (\( \mu \), \( p \)) but the context indicates \( p \) represents proportion. For the purpose of this educational webpage, precise selection for hypotheses must consider the claim being tested.

given data claim :p<0.10α=0.025we have to complete the hypothesis testing for the given data,

Answered: Test the claim that the proportion 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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Test the claim that the proportion of men who own cats is smaller than the proportion of women who own cats at the .005 significance level.The null and alternative hypothesis would be: H0:μM=μFH0:μM=μFH1:μM>μFH1:μM>μF H0:pM=pFH0:pM=pFH1:pM<pFH1:pM<pF H0:μM=μFH0:μM=μFH1:μM≠μFH1:μM≠μF H0:μM=μFH0:μM=μFH1:μM<μFH1:μM<μF H0:pM=pFH0:pM=pFH1:pM>pFH1:pM>pF H0:pM=pFH0:pM=pFH1:pM≠pFH1:pM≠pF The test is: left-tailed two-tailed right-tailed Based on a sample of 20 men, 30% owned catsBased on a sample of 60 women, 50% 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
Test the claim that the proportion of people who own cats is larger than 70% at the 0.025 significance level.The null and alternative hypothesis would be: H0:μ≥0.7H0:μ≥0.7H1:μ<0.7H1:μ<0.7 H0:p≥0.7H0:p≥0.7H1:p<0.7H1:p<0.7 H0:p≤0.7H0:p≤0.7H1:p>0.7H1:p>0.7 H0:μ≤0.7H0:μ≤0.7H1:μ>0.7H1:μ>0.7 H0:μ=0.7H0:μ=0.7H1:μ≠0.7H1:μ≠0.7 H0:p=0.7H0:p=0.7H1:p≠0.7H1:p≠0.7 The test is: right-tailed left-tailed two-tailed Based on a sample of 600 people, 75% owned catsThe 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 men who own cats is smaller than the proportion of women who own cats at the .05 significance level.The null and alternative hypothesis would be: H0:μM=μFH1:μM<μF H0:pM=pFH1:pM<pF H0:pM=pFH1:pM>pF H0:pM=pFH1:pM≠pF H0:μM=μFH1:μM≠μF H0:μM=μFH1:μM>μF The test is: right-tailed left-tailed two-tailed Based on a sample of 20 men, 40% owned catsBased on a sample of 60 women, 55% owned catsThe test statistic is:  (to 2 decimals)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 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
Test the claim that the proportion of men who own cats is larger than 70% at the .025 significance level.The null and alternative hypothesis would be: H0:μ=0.7H0:μ=0.7H1:μ≠0.7H1:μ≠0.7 H0:p=0.7H0:p=0.7H1:p>0.7H1:p>0.7 H0:p=0.7H0:p=0.7H1:p<0.7H1:p<0.7 H0:p=0.7H0:p=0.7H1:p≠0.7H1:p≠0.7 H0:μ=0.7H0:μ=0.7H1:μ>0.7H1:μ>0.7 H0:μ=0.7H0:μ=0.7H1:μ<0.7H1:μ<0.7 The test is: right-tailed two-tailed left-tailed Based on a sample of 100 people, 79% owned catsThe test statistic is:  (to 2 decimals)The critical 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 larger than 10% at the .10 significance level.The null and alternative hypothesis would be: H0:p=0.1H0:p=0.1H1:p>0.1H1:p>0.1 H0:μ=0.1H0:μ=0.1H1:μ<0.1H1:μ<0.1 H0:μ=0.1H0:μ=0.1H1:μ>0.1H1:μ>0.1 H0:p=0.1H0:p=0.1H1:p≠0.1H1:p≠0.1 H0:μ=0.1H0:μ=0.1H1:μ≠0.1H1:μ≠0.1 H0:p=0.1H0:p=0.1H1:p<0.1H1:p<0.1 The test is: right-tailed left-tailed two-tailed Based on a sample of 45 people, 15% owned catsThe test statistic is:  (to 2 decimals)The critical value is:  (to 2 decimals)Based on this we: Reject the null hypothesis Fail to reject the null hypothesis
Test the claim that the mean GPA of night students is larger than 2.4 at the 0.025 significance level. The null and alternative hypothesis would be: Ho p≥ 0.6 Ho:μ ≤ 2.4 Ho:p ≤ 0.6 H₁ p 2.4 H₁:p > 0.6 Ho:. :p= 0.6 Ho:} > 2.4 Ho: = 2.4 H₁:p‡ 0.6 H₁:μ< 2.4 H₁:µ ‡ 2.4 The test is: two-tailed left-tailed right-tailed Based on a sample of 60 people, the sample mean GPA was 2.41 with a standard deviation of 0.02 The p-value is: (to 2 decimals) Based on this we: O Fail to reject the null hypothesis O Reject the null hypothesis
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.
Test the claim that the proportion of men who own cats is smaller than 70% at the 0.05 significance level.The null and alternative hypothesis would be: H0:p≤0.7H0:p≤0.7H1:p>0.7H1:p>0.7 H0:μ=0.7H0:μ=0.7H1:μ≠0.7H1:μ≠0.7 H0:p=0.7H0:p=0.7H1:p≠0.7H1:p≠0.7 H0:μ≥0.7H0:μ≥0.7H1:μ<0.7H1:μ<0.7 H0:μ≤0.7H0:μ≤0.7H1:μ>0.7H1:μ>0.7 H0:p≥0.7H0:p≥0.7H1:p<0.7H1:p<0.7 The test is: right-tailed two-tailed left-tailed Based on a sample of 800 people, 67% 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
Test the claim that the proportion of people who own cats is significantly different than 80% at the 0.2 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: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 H0:p=0.8H0:p=0.8H1:p≠0.8H1:p≠0.8 The test is: two-tailed right-tailed left-tailed Based on a sample of 300 people, 74% owned catsThe test statistic is:  (to 2 decimals)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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