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In Exercises 9–12, test the claim about the difference between two population
12. Claim: μ1 > μ2; α = 0.01, Assume
Sample statistics:
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Elementary Statistics: Picturing the World (6th Edition)
- In Exercises 5–20, assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. (Note: Answers in Appendix D include technology answers based on Formula 9-1 along with “Table” answers based on Table A-3 with df equal to the smaller of n1 − 1 and n2 − 1.) Car and Taxi Ages When the author visited Dublin, Ireland (home of Guinness Brewery employee William Gosset, who first developed the t distribution), he recorded the ages of randomly selected passenger cars and randomly selected taxis. The ages can be found from the license plates. (There is no end to the fun of traveling with the author.) The ages (in years) are listed below. We might expect that taxis would be newer, so test the claim that the mean age of cars is greater than the mean age of taxis.arrow_forwardTest the claim that the proportion of men who own cats is smaller than 70% at the 0.01 significance level. The null and alternative hypothesis would be: 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 H0:p=0.7H0:p=0.7H1:p≠0.7H1:p≠0.7 Correct The test is: left-tailed right-tailed two-tailed Correct Based on a sample of 300 people, 69% owned cats 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 hypothesisarrow_forwardTest the claim that the proportion of people who own cats is smaller than 50% at the 0.01 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: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 The test is: left-tailed two-tailed right-tailed Based on a sample of 100 people, 49% owned catsThe test statistic is: (Round to 2 decimals)The p-value is: (Round to 2 decimals)Based on this we:arrow_forward
- In Exercise 4.2.27, in finding a confidence interval for the ratio of thevariances of two normal distributions, we used a statistic S21/S22, which has an Fdistributionwhen those two variances are equal. If we denote that statistic by F,we can test H0 : σ21 = σ22 against H1 : σ21 > σ22 using the critical region F ≥ c. Ifn = 13, m = 11, and α = 0.05, find c.arrow_forwardTest the claim that the proportion of men who own cats is smaller than 80% at the 0.01 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: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≥0.8H0:μ≥0.8H1:μ<0.8H1:μ<0.8 The test is: left-tailed right-tailed two-tailed Based on a sample of 700 people, 74% 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 hypothesisarrow_forwardTest 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 hypothesisarrow_forward
- Test the claim that the proportion of people who own cats is larger than 60% at the 0.01 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: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 H0:p≥0.6H0:p≥0.6H1:p<0.6H1:p<0.6 The test is: left-tailed right-tailed two-tailed Based on a sample of 100 people, 67% owned catsThe p-value is: (to 2 decimals)Based on this we: Reject the null hypothesis Fail to reject the null hypothesisarrow_forwardConduct a test at the alphaαequals=0.010.01 level of significance by determining (a) the null and alternative hypotheses, (b) the test statistic, and (c) the P-value. Assume the samples were obtained independently from a large population using simple random sampling. Test whether p 1 greater than p 2p1>p2. The sample data are x 1 equals 127x1=127, n 1 equals 248n1=248, x 2 equals 134x2=134, and n 2 equals 318n2=318.arrow_forwardTest the claim that the proportion of people who own cats is smaller than 60% at the 0.005 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: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 The test is: two-tailed right-tailed left-tailed Based on a sample of 200 people, 51% 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 hypothesisarrow_forward
- Conduct a test at the alphaαequals=0.010.01 level of significance by determining (a) the null and alternative hypotheses, (b) the test statistic, and (c) the P-value. Assume the samples were obtained independently from a large population using simple random sampling. Test whether p 1 greater than p 2p1>p2. The sample data are x 1 equals 128x1=128, n 1 equals 247n1=247, x 2 equals 140x2=140, and n 2 equals 311n2=311. (a) Choose the correct null and alternative hypotheses below. A. Upper H 0 : p 1 equals p 2H0: p1=p2 versus Upper H 1 : p 1 less than p 2H1: p1<p2 B. Upper H 0 : p 1 equals 0H0: p1=0 versus Upper H 1 : p 1 not equals 0H1: p1≠0 C. Upper H 0 : p 1 equals p 2H0: p1=p2 versus Upper H 1 : p 1 greater than p 2H1: p1>p2 D. Upper H 0 : p 1 equals p 2H0: p1=p2 versus Upper H 1 : p 1 not equals p 2H1: p1≠p2 (b) Determine the test statistic. z0equals=nothing (Round to two decimal places as needed.) (c) Determine…arrow_forwardConduct a test at the alphaαequals=0.100.10 level of significance by determining (a) the null and alternative hypotheses, (b) the test statistic, and (c) the P-value. Assume the samples were obtained independently from a large population using simple random sampling. Test whether p 1 greater than p 2 p1>p2. The sample data are x 1 =121 n 1 =257 x 2 =133 n 2 =303arrow_forwardIn a test of H0: p = 0.8 against H1: p ≠ 0.8, a sample of size 1000 produces Z = 2.05 for the value of the test statistic. Thus the p-value (or observed level of significance) of the test is approximately equal to:arrow_forward
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