### Hypothesis Testing for Mean GPA#### Problem Statement:Test the claim that the mean GPA of night students is significantly different than 3.3 at the 0.2 significance level.#### Hypotheses:The null and alternative hypotheses would be:\[H_0: \mu = 3.3\]\[H_1: \mu \neq 3.3\]#### Nature of the Test:This test is **two-tailed**.#### Sample Data:Based on a sample of 25 people, the sample mean GPA was 3.34 with a standard deviation of 0.04.#### Test Statistic Calculation:\[ \text{The test statistic is:} \ \boxed{} \ (to 2 decimals)\]#### P-value Calculation:\[ \text{The p-value is:} \ \boxed{} \ (to 2 decimals)\]#### Conclusion:Based on this we:- [ ] Fail to reject the null hypothesis- [ ] Reject the null hypothesisSelect one based on the calculated p-value and test statistic.

Given that Sample size n =25 Sample mean =3.34 Standard deviation =0.04

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 mean GPA of night students is significantly different than 2 at the 0.2 significance level.The null and alternative hypothesis would be: H0:μ≥2H0:μ≥2H1:μ<2H1:μ<2 H0:μ≤2H0:μ≤2H1:μ>2H1:μ>2 H0:p≥0.5H0:p≥0.5H1:p<0.5H1:p<0.5 H0:p=0.5H0:p=0.5H1:p≠0.5H1:p≠0.5 H0:p≤0.5H0:p≤0.5H1:p>0.5H1:p>0.5 H0:μ=2H0:μ=2H1:μ≠2H1:μ≠2 The test is: right-tailed two-tailed left-tailed Based on a sample of 25 people, the sample mean GPA was 1.97 with a standard deviation of 0.06The p-value is: (to 2 decimals)Based on this we: Fail to reject the null hypothesis Reject the null hypothesis
A medical equipment manufacturer believes that the proportion of faulty blood pressure monitors is greater than 0.11, the proportion stated by the supplier. We perform a hypothesis test at a significance level of 0.05 with the null and alternative hypothesis as follows: Ho: p = 0.11 and Ha: p < 0.11. A researcher inspects 150 items and finds 25 faulty ones. She gives a p-value of 0.01 in her analysis. Which of the following definitions is the correct interpretation of the p-value? O The probability of getting 25 or more faulty blood pressure monitors out of 150 if the true faulty rate is 0.11. The value that the z-statistic must be less than in order to reject the null hypothesis. The probability of rejecting a true null hypothesis. O The probability that the true rate of faulty items is 0.01.
Test the claim that the proportion of people who own cats is significantly diffe significance level. The null and alternative hypothesis would be: Ο Η: μ 0.9 Ο H: μ > 0.9 Ha:µ 0.9 На:р 0.9 The test is: O two-tailed O right-tailed O left-tailed Based on a sample of 300 people, 88% owned cats The test statistic is: (Round to 2 decimals) The p-value is: (Round to 2 decimals) Based on this we: O Do not reject the null hypothesis O 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 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 mean GPA of night students is larger than the mean GPA of day students at the 0.10 significance level.The null and alternative hypothesis would be: H0:μN=μDH1:μN≠μD H0:pN≥pDH1:pN<pD H0:μN≤μDH1:μN>μD H0:pN≤pDH1:pN>pD H0:μN≥μDH1:μN<μD H0:pN=pDH1:pN≠pD The test is: two-tailed right-tailed left-tailed The sample consisted of 80 night students, with a sample mean GPA of 3.36 and a standard deviation of 0.08, and 80 day students, with a sample mean GPA of 3.35 and a standard deviation of 0.04.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 mean GPA of night students is smaller than 3.1 at the 0.025 significance level.The null and alternative hypothesis would be: H0:μ≤3.1H0:μ≤3.1H1:μ>3.1H1:μ>3.1 H0:p≥0.775H0:p≥0.775H1:p<0.775H1:p<0.775 H0:μ=3.1H0:μ=3.1H1:μ≠3.1H1:μ≠3.1 H0:p≤0.775H0:p≤0.775H1:p>0.775H1:p>0.775 H0:p=0.775H0:p=0.775H1:p≠0.775H1:p≠0.775 H0:μ≥3.1H0:μ≥3.1H1:μ<3.1H1:μ<3.1 The test is: two-tailed left-tailed right-tailed Based on a sample of 80 people, the sample mean GPA was 3.05 with a standard deviation of 0.08The 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 mean GPA of night students is smaller than 2.8 at the .05 significance level. The null and alternative hypothesis would be: = 2.8 Ho:p= 0.7 Ho:μ = 2.8 : Ho p= 0.7 Ho:μ = 2.8 Ho: p = 0.7 Ho:μ = H₁:p 2.8 H₁:p 0.7 H₁:μ 0.7 H₁:μ ‡ 2.8 The test is: right-tailed two-tailed left-tailed Based on a sample of 50 people, the sample mean GPA was 2.75 with a standard deviation of 0.02 The 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
I randomly sample 219 students and ask them to provide their USF GPA. I wish to determine if the average GPA of all USF students ex mu + 3.25 ceeds 3.25. Unfortunately, I generated the printout shown here: One-Sample T Test Null Hypothesis: H - 3.25 Alternative Hyp: u- 3.25 Variable Mean SE DF GPA 3.3121 0.0340 1.82 218 0.0694 Cases Included 219 What assumption is needed for this analysis to be valid? None. The Central Limit Theorem applies and no other assumptions are needed. The GPAS of all USF students need to be approximately normally distributed The mean GPA of all USF students need to be approximately normally distributed
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

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