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=2 HA:μ≠2HA:μ≠2 H0:p≤0.5H0:p≤0.5 HA:p>0.5HA:p>0.5 H0:p≥0.5H0:p≥0.5 HA:p<0.5HA:p<0.5 H0:μ≥2H0:μ≥2 HA:μ<2HA:μ<2 H0:μ≤2H0:μ≤2 HA:μ>2HA:μ>2 H0:p=0.5H0:p=0.5 HA:p≠0.5HA:p≠0.5 The test is: right-tailed two-tailed left-tailed Based on a sample of 50 people, the sample mean GPA was 1.95 with a standard deviation of 0.05 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 significantly different than 2 at the 0.2 significance level. The null and alternative hypothesis would be: H0:μ=2H0:μ=2 HA:μ≠2HA:μ≠2 H0:p≤0.5H0:p≤0.5 HA:p>0.5HA:p>0.5 H0:p≥0.5H0:p≥0.5 HA:p<0.5HA:p<0.5 H0:μ≥2H0:μ≥2 HA:μ<2HA:μ<2 H0:μ≤2H0:μ≤2 HA:μ>2HA:μ>2 H0:p=0.5H0:p=0.5 HA:p≠0.5HA:p≠0.5 The test is: right-tailed two-tailed left-tailed Based on a sample of 50 people, the sample mean GPA was 1.95 with a standard deviation of 0.05 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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Description: 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=2HA:μ≠2HA:μ≠2H0:p≤0.5H0:p≤0.5HA:p>0.5HA:p>0.5H0:p≥0.5H0:p≥0.5HA:p<0.5HA:p<0.5H

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Test the claim that the proportion of people who own cats is significantly different than 40% at the 0.01 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: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 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 100 people, 48% 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 .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 mean GPA of night students is significantly different than the mean GPA of day students at the 0.2 significance level.The null and alternative hypothesis would be: H0:μN≤μDH0:μN≤μDH1:μN>μDH1:μN>μD H0:pN≤pDH0:pN≤pDH1:pN>pDH1:pN>pD H0:pN≥pDH0:pN≥pDH1:pN<pDH1:pN<pD H0:pN=pDH0:pN=pDH1:pN≠pDH1:pN≠pD H0:μN≥μDH0:μN≥μDH1:μN<μDH1:μN<μD H0:μN=μDH0:μN=μDH1:μN≠μDH1:μN≠μD The test is: right-tailed two-tailed left-tailed The sample consisted of 25 night students, with a sample mean GPA of 2.27 and a standard deviation of 0.06, and 25 day students, with a sample mean GPA of 2.31 and a standard deviation of 0.03.The 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 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 2.1 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 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 mean GPA of night students is smaller than the mean GPA of day students at the 0.01 significance level.The null and alternative hypothesis would be: H0:μN=μDH0:μN=μDH1:μN≠μDH1:μN≠μD H0:μN≤μDH0:μN≤μDH1:μN>μDH1:μN>μD H0:pN=pDH0:pN=pDH1:pN≠pDH1:pN≠pD H0:pN≥pDH0:pN≥pDH1:pN<pDH1:pN<pD H0:μN≥μDH0:μN≥μDH1:μN<μDH1:μN<μD H0:pN≤pDH0:pN≤pDH1:pN>pDH1:pN>pD The test is: left-tailed right-tailed two-tailed The sample consisted of 45 night students, with a sample mean GPA of 3.23 and a standard deviation of 0.05, and 45 day students, with a sample mean GPA of 3.26 and a standard deviation of 0.08.The test statistic is:  (to 2 decimals)The p-value is:  (to 2 decimals)Based on this we:
Test the claim that the mean GPA of Orange Coast students is larger than the mean GPA of Coastline students at the 0.01 significance level.The null and alternative hypothesis would be: H0:μO≤μCH0:μO≤μCH1:μO>μCH1:μO>μC H0:μO=μCH0:μO=μCH1:μO≠μCH1:μO≠μC H0:μO≥μCH0:μO≥μCH1:μO<μCH1:μO<μC H0:pO≤pCH0:pO≤pCH1:pO>pCH1:pO>pC H0:pO=pCH0:pO=pCH1:pO≠pCH1:pO≠pC H0:pO≥pCH0:pO≥pCH1:pO<pCH1:pO<pC The test is: two-tailed right-tailed left-tailed The sample consisted of 75 Orange Coast students, with a sample mean GPA of 3.32 and a standard deviation of 0.03, and 75 Coastline students, with a sample mean GPA of 3.3 and a standard deviation of 0.08.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