### Hypothesis Testing: Mean GPA of Night Students#### Problem Statement:Test the claim that the mean GPA of night students is larger than 3.3 at the 0.005 significance level.#### Null and Alternative Hypothesis:The null and alternative hypothesis would be:- $H_0: \mu \leq 3.3$- $H_1: \mu > 3.3$#### Nature of the Test:The test is:- Right-tailed#### Sample Data:Based on a sample of 50 people, the sample mean GPA was 3.33 with a standard deviation of 0.06.#### P-Value:The p-value is: [Input p-value here] (to 2 decimals)#### Conclusion:Based on this, we:- Reject the null hypothesis- Fail to reject the null hypothesis**Note:** Actual p-value and conclusion depend on further statistical computations.

Answered: Image /qna-images/answer/f423663c-d0e1-4112-95c1-5e5436245ae8.jpg

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 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
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Test the claim that the mean GPA of night students is significantly different than 3.4 at the 0.2 significance level.The null and alternative hypotheses would be: 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: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:μ=3.4H0:μ=3.4H1:μ≠3.4H1:μ≠3.4 Based on a sample of 31 people, the sample mean GPA was 3.37 with a standard deviation of 0.08The p-value is:  (to 3 decimals)The positive significance level is:  (to 2 decimals)
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 mean GPA of night students is significantly different than 3.2 at the 0.05 significance level.The null and alternative hypothesis would be: H0:μ≤3.2H0:μ≤3.2H1:μ>3.2H1:μ>3.2 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≥3.2H0:μ≥3.2H1:μ<3.2H1:μ<3.2 H0:p=0.8H0:p=0.8H1:p≠0.8H1:p≠0.8 H0:μ=3.2H0:μ=3.2H1:μ≠3.2H1:μ≠3.2 The test is: right-tailed two-tailed left-tailed Based on a sample of 65 people, the sample mean GPA was 3.16 with a standard deviation of 0.05The 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 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 mean GPA of night students is smaller than 2.1 at the 0.025 significance level.The null and alternative hypothesis would be: H0:μ=2.1H0:μ=2.1H1:μ≠2.1H1:μ≠2.1 H0:p≤0.525H0:p≤0.525H1:p>0.525H1:p>0.525 H0:μ≤2.1H0:μ≤2.1H1:μ>2.1H1:μ>2.1 H0:p≥0.525H0:p≥0.525H1:p<0.525H1:p<0.525 H0:μ≥2.1H0:μ≥2.1H1:μ<2.1H1:μ<2.1 H0:p=0.525H0:p=0.525H1:p≠0.525H1:p≠0.525 The test is: right-tailed two-tailed left-tailed Based on a sample of 40 people, the sample mean GPA was 2.06 with a standard deviation of 0.04The 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 mean GPA of night students is smaller than the mean GPA of day students at the 0.005 significance level.The null and alternative hypothesis would be: H0:pN=pDH1:pN≠pD H0:pN≥pD H1:pN<pD H0:μN≥μD H1:μN<μD H0:μN≤μD H1:μN>μD H0:pN≤pDH1:pN>pD H0:μN=μDH1:μN≠μD The test is: two-tailed left-tailed right-tailed The sample consisted of 70 night students, with a sample mean GPA of 2.16 and a standard deviation of 0.07, and 70 day students, with a sample mean GPA of 2.18 and a standard deviation of 0.06. The 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 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

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