**Test the Claim about Night Students' Mean GPA at 0.10 Significance Level****Objective**: Test the claim that the mean GPA of night students is larger than 3.1 at the 0.10 significance level.**Hypotheses Selection**:- **Null Hypothesis (\(H_0\))**: \(\mu = 3.1\)- **Alternative Hypothesis (\(H_1\))**: \(\mu > 3.1\)**Type of Test**: - Right-tailed**Sample Information**:- Sample size: 75 people- Sample mean GPA: 3.12- Standard deviation: 0.05**Statistical Analysis**:- **Test Statistic**: \( \_\_\_\_\_\_ \) (to 2 decimals)- **P-value**: \( \_\_\_\_\_\_ \) (to 2 decimals)**Decision**:- Based on the results, choose one of the following: - Reject the null hypothesis - Fail to reject the null hypothesisUse this layout to input and interpret statistical data related to hypothesis testing in educational contexts.

Assume that μ is the mean GPA of all night students.

Answered: Test the claim that the mean GPA 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 significantly different than the proportion of women who own cats at the 0.2 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 40 men, 30% owned catsBased on a sample of 60 women, 35% 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 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: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: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 The test is: left-tailed two-tailed right-tailed Based on a sample of 400 people, 77% 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 men who own cats is significantly different than 60% at the 0.02 significance level.The null and alternative hypothesis would be: H0:μ=0.6H0:μ=0.6H1:μ<0.6H1:μ<0.6 H0:p=0.6H0:p=0.6H1:p>0.6H1:p>0.6 H0:p=0.6H0:p=0.6H1:p<0.6H1:p<0.6 H0:μ=0.6H0:μ=0.6H1:μ≠0.6H1:μ≠0.6 H0:μ=0.6H0:μ=0.6H1:μ>0.6H1:μ>0.6 H0:p=0.6H0:p=0.6H1:p≠0.6H1:p≠0.6 The test is: two-tailed right-tailed left-tailed Based on a sample of 60 people, 66% owned catsThe test statistic is: (to 2 decimals)The positive critical 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 mean GPA of night students is larger than 2.6 at the .025 significance level.The null and alternative hypothesis would be: H0:μ=2.6H0:μ=2.6H1:μ>2.6H1:μ>2.6 H0:p=0.65H0:p=0.65H1:p<0.65H1:p<0.65 H0:p=0.65H0:p=0.65H1:p≠0.65H1:p≠0.65 H0:μ=2.6H0:μ=2.6H1:μ≠2.6H1:μ≠2.6 H0:μ=2.6H0:μ=2.6H1:μ<2.6H1:μ<2.6 H0:p=0.65H0:p=0.65H1:p>0.65H1:p>0.65 The test is: two-tailed left-tailed right-tailed Based on a sample of 30 people, the sample mean GPA was 2.64 with a standard deviation of 0.03The 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 clainm that the mean GPA of night students is significantly different than 2.5 at the 0.01 significance level. The null and alternative hypothesis would be: Ho:u > 2.5 Ho:p 0.625 Ho:p 0.625 H1:µ> 2.5 H :µ+ 2.5 H1:p 0.625 The test is: right-tailed left-tailed two-tailed Based on a sample of 55 people, the sample mean GPA was 2.46 with a standard deviation of 0.07 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 mean GPA of night students is smaller than 3.4 at the .005 significance level.The null and alternative hypothesis would be: H0:p=0.85H0:p=0.85H1:p>0.85H1:p>0.85 H0:p=0.85H0:p=0.85H1:p≠0.85H1:p≠0.85 H0:μ=3.4H0:μ=3.4H1:μ≠3.4H1:μ≠3.4 H0:p=0.85H0:p=0.85H1:p<0.85H1:p<0.85 H0:μ=3.4H0:μ=3.4H1:μ>3.4H1:μ>3.4 H0:μ=3.4H0:μ=3.4H1:μ<3.4H1:μ<3.4 The test is: -left-tailed -two-tailed -right-tailed Based on a sample of 20 people, the sample mean GPA was 3.35 with a standard deviation of 0.08The 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
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