### Hypothesis Testing Example: Mean GPA of Night Students#### Problem:Test the claim that the mean GPA of night students is smaller than 2.8 at the 0.05 significance level.#### Null and Alternative Hypothesis:The null and alternative hypothesis would be:- Null Hypothesis (\( H_0 \)): \( \mu = 2.8 \)- Alternative Hypothesis (\( H_1 \)): \( \mu < 2.8 \)This setup corresponds to a **left-tailed test**.#### Sample Data:Based on a sample of 50 people, the sample mean GPA was 2.75 with a standard deviation of 0.02.#### Steps to Solve:1. **Calculate the Test Statistic**: - Formula: \[ Z = \frac{{\bar{X} - \mu}}{{\frac{\sigma}{\sqrt{n}}}} \] - Where: \(\bar{X}\) = Sample mean = 2.75 \(\mu\) = Population mean = 2.8 \(\sigma\) = Sample standard deviation = 0.02 \(n\) = Sample size = 502. **Determine the Critical Value** at the 0.05 significance level for a left-tailed test.3. **Decision Rule**: - Compare the test statistic to the critical value to determine whether to reject the null hypothesis.#### Calculation Inputs:- **Test Statistic Calculation**: \( \_\_\_\_\_\@\)- **Critical Value Lookup**: \( \_\_\_\_\_\@\)#### Conclusion:Based on the calculated test statistic and the critical value, we will either:- **Reject the null hypothesis**- **Fail to reject the null hypothesis**Please refer to statistical tables or software to find the exact critical value and to perform the precise calculations needed to find the test statistic. This will help in making the final decision regarding the hypothesis.

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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 people who own cats is significantly different than 50% at the 0.01 significance level.The null and alternative hypothesis would be: H0:p=0.5H0:p=0.5H1:p≠0.5H1:p≠0.5 H0:μ=0.5H0:μ=0.5H1:μ≠0.5H1:μ≠0.5 H0:p≤0.5H0:p≤0.5H1:p>0.5H1:p>0.5 H0:μ≥0.5H0:μ≥0.5H1:μ<0.5H1:μ<0.5 H0:p≥0.5H0:p≥0.5H1:p<0.5H1:p<0.5 H0:μ≤0.5H0:μ≤0.5H1:μ>0.5H1:μ>0.5 The test is: left-tailed two-tailed right-tailed Based on a sample of 700 people, 43% 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 the proportion of women who own cats at the .10 significance level. The null and alternative hypothesis would be: Ho: HM = HF Ho: HM = PF Ho:PM = PF Ho PM = PF Ho: PM = µf Ho:PM = PF H:PM > HF H:UM HF H:PM > PF H1:PM < Pf H1: µM < µp H1:PM + PF %3D The test is: right-tailed two-tailed left-tailed Based on a sample of 60 men, 25% owned cats Based on a sample of 80 women, 50% owned cats 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 the proportion of women who own cats at the .10 significance level. The null and alternative hypothesis would be: Ho: M = μF Ho: PM = PF Ho: PM = PF Ho: PM = PF Ho: M = μF Ho: M = μF H₁ μM PF H₁:PM > PF H₁:PM PF H₁:PM ME O O The test is: two-tailed right-tailed left-tailed O Based on a sample of 40 men, 25% owned cats Based on a sample of 40 women, 35% owned cats The test statistic is: decimals) The critical value is: O Reject the null hypothesis O Fail to reject the null hypothesis (to 2 decimals) Based on this we: (to 2
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
Test the claim that the proportion of people who own cats is significantly different than 20% at the 0.02 significance level.The null and alternative hypothesis would be: H0:p=0.2H0:p=0.2H1:p≠0.2H1:p≠0.2 H0:μ≤0.2H0:μ≤0.2H1:μ>0.2H1:μ>0.2 H0:μ=0.2H0:μ=0.2H1:μ≠0.2H1:μ≠0.2 H0:μ≥0.2H0:μ≥0.2H1:μ<0.2H1:μ<0.2 H0:p≥0.2H0:p≥0.2H1:p<0.2H1:p<0.2 H0:p≤0.2H0:p≤0.2H1:p>0.2H1:p>0.2 Correct The test is: left-tailed two-tailed right-tailed Correct Based on a sample of 100 people, 29% 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 men who own cats is significantly different than 15% at the 0.01 significance level. The null and alternative hypothesis would be: Ho:p 0.15 Ho:p= 0.15 Ho:u = Ho:u= Ho:= Ho:p 0.15 o H1:p> 0.15 H:p H:p# H: < H:p 0.15 |3D %3D O.
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
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Test the claim that the proportion of people who own cats is significantly different than 80% at the 0.02 significance level. The null and alternative hypothesis would be: Ho:µ 0.8 Ho:p= 0.8 Ho:µ = 0.8 Ho:p > 0.8 H1:µ > 0.8 H1:p > 0.8 H1:µ < 0.8 H1:p 0.8 H1:µ + 0.8 H1:p < 0.8 The test is: two-tailed right-tailed left-tailed Based on a sample of 100 people, 84% owned cats (to 2 decimals) The p-value is: Based on this we: Fail to reject the null hypothesis Reject the null hypothesis
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