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In Exercises 9–12, test the claim about the difference between two population means μ1 and μ2 at the level of significance α. Assume the samples are random and independent, and the populations are
9. Claim: μ1 = μ2; α = 0.01, Assume,
Sample statistics:
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Elementary Statistics: Picturing the World (6th Edition)
- Test the claim that the proportion of people who own cats is smaller than 10% at the 0.025 significance level.The null and alternative hypothesis would be: H0:μ≥0.1H0:μ≥0.1Ha:μ<0.1Ha:μ<0.1 H0:p≤0.1H0:p≤0.1Ha:p>0.1Ha:p>0.1 H0:μ≤0.1H0:μ≤0.1Ha:μ>0.1Ha:μ>0.1 H0:μ=0.1H0:μ=0.1Ha:μ≠0.1Ha:μ≠0.1 H0:p=0.1H0:p=0.1Ha:p≠0.1Ha:p≠0.1 H0:p≥0.1H0:p≥0.1Ha:p<0.1Ha:p<0.1 The test is: right-tailed left-tailed two-tailed Based on a sample of 600 people, 2% owned catsThe test statistic is: (Round to 2 decimals)The p-value is: (Round to 2 decimals)Based on this we: Do not reject the null hypothesis Reject the null hypothesisarrow_forward3) A firm in Lebanon has developed a chemical solution that can be added to car gasolinewhich they believe will increase the miles per gallon that cars will get. The owners areinterested in estimating the difference between mean mpg for cars using the chemicalsolution versus those that are not using the solution. The following data represent the mpgfor independent random samples of cars from each population.with Solution without Solution______________________________n1 = 36 n2 = 42 x1 = 25.45 x2 = 24.1 _______________________________Assume that the populations are normally distributed and the population standarddeviations are known to be σ1 = 3.95 (with solution) and σ2 = 3.09 (without solution).Given this data, can the owners believe that there is a difference between mean mpg forcars using the chemical solution versus those that are not using the solution? Test using analpha level equal to 0.05.4) Given the following null and alternative hypothesis:H0: σ 2 ≤ 52HA : σ 2 > 52and the…arrow_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
- Daily anxiety was measured on a scale from 1 (not at all anxious) to 5 (very anxious) in a random sample of 2000 city dwellers from across the U.S. They found that M = 4.13, 95% CIs [4.06, 4.20].How would you interpret these results? What conclusions would you draw about the precision of the point estimate? What statistical decision would have been made in this scenario if the researchers employed Null Hypothesis Significance Testing instead of the New Stats?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_forwardGiven sample sizes n1 = n2 = 10, sample means = 5.2 and =7.1, and sample variances = 4 and = 6.2 using alpha = 0.05, test the hypothesis H0: u1 = u2 against Ha: u1 does not equal u2. A) What assumptions do we need to make about the data to use the central limit theorem? B) What is the value of the appropriate test statisctics?arrow_forward
- Assume that you have a sample of n1=8, with the sample mean X1=44, and a sample standard deviation of S1=5, and you have an independent sample of n2=14 from another population with a sample mean of X2=30 and the sample standard deviation S2=6. Using a significance level of α=0.025, what is the critical value for a one-tail test of the hypothesis H0: μ1≤ μ2 against the alternative H1: μ1>μ2? The critical value is ______ (Round to two decimal places as needed.)arrow_forwardTest the claim that the mean GPA of night students is smaller than 2.2 at the .05 significance level.The null and alternative hypothesis would be: H0:p=0.55H0:p=0.55H1:p≠0.55H1:p≠0.55 H0:p=0.55H0:p=0.55H1:p<0.55H1:p<0.55 H0:μ=2.2H0:μ=2.2H1:μ≠2.2H1:μ≠2.2 H0:p=0.55H0:p=0.55H1:p>0.55H1:p>0.55 H0:μ=2.2H0:μ=2.2H1:μ<2.2H1:μ<2.2 H0:μ=2.2H0:μ=2.2H1:μ>2.2H1:μ>2.2 The test is: right-tailed two-tailed left-tailed Based on a sample of 35 people, the sample mean GPA was 2.15 with a standard deviation of 0.06The test statistic is (to 3 decimals)The critical value is (to 3 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 larger than 60% at the 0.05 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: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 The test is: two-tailed left-tailed right-tailed Based on a sample of 200 people, 69% owned catsThe 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=0.100.10 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_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_forwardIn 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.) Are Male Professors and Female Professors Rated Differently? Listed below are student evaluation scores of female professors and male professors from Data Set 17 “Course Evaluations” in Appendix B. Test the claim that female professors and male professors have the same mean evaluation ratings. Does there appear to be a difference?arrow_forward
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