ANOVA Checkpoint Question 1 Select one answer. 10 points To determine whether there is a relationship between the type of school attended and verbal reasoning scores for Irish students, three samples with 25 students, in each group, were randomly selected from data used by Raferty and Hout (1985). One group of students attended secondary school, the second group of students attended vocational school, and the third group consisted of students who attended only primary school. Raftery, A. E.2 and Hout, M. (1985). Does Irish education approach the meritocratic ideal? A logistic analysis. Economic and Social Review, 16, 115-140. Here are the three sample standard deviations for the verbal reasoning scores for the three groups (secondary school, vocational school, and primary school only): Based on this information, do the data meet the condition of equal population standard deviations for the use of the ANOVA? Yes, because 14.18 11.71 < 2. Yes, because 14.18/11.71 < 2. No, because the standard deviations are not equal. Question 2 Select one answer. 10 points A medical school admissions officer was interested in whether there is a difference in MCAT test scores (the standardized test used for medical school admission) between (1) biological sciences majors, (2) social science majors and (3) math majors. The admissions officer randomly sampled 50 students from each of these majors who applied to medical school in 2014 and recorded their MCAT score. Let 1, 2, and 3 be the MCAT scores for students who majored in biological sciences, social sciences, and math, respectively. Which of the following are the appropriate null and alternative hypotheses? H0: 1 = 2 = 3 Ha: 1, 2, 3, are not all equal H0: 1, 2, 3, are not all equal Ha: 1 = 2 = 3 H0: 1 = 2 = 3 Ha: 1 2 3 H0: 1 2 3 Ha: 1 = 2 = 3 Question 3 Select one answer. 10 points A medical school admissions officer was interested in whether there is a difference in MCAT test scores (the standardized test used for medical school admission) between (1) biological sciences majors, (2) social science majors and (3) math majors. The admissions officer randomly sampled 50 students from each of these majors who applied to medical school in 2014 and recorded their MCAT score. The following hypotheses were tested: H0: 1 = 2 = 3 Ha: 1, 2, 3, are not all equal The analysis was run on the data and the following output was obtained: ANOVA Table Source DF SS MS F-Stat P-Value Treatments 2 304.11487 152.05743 5.1196003 0.0071 Error 147 4366.0523 29.701036 Total 149 4670.1672 Which of the following is an appropriate conclusion based on the output? Fail to reject H0 and conclude that the data provide strong evidence that the three mean MCAT scores (representing the three majors) are not all equal. Fail to reject H0 and conclude that the data do not provide sufficient evidence that there is a relationship between the student's major and MCAT score. Reject H0 and conclude that the data provide strong evidence that there is a relationship between the student's major and MCAT score. Reject H0 and conclude that the data provide strong evidence that MCAT scores are related to student majors in the following way: the mean MCAT score for math majors is higher than the mean MCAT score for biological sciences majors, which in turn is higher than that of social sciences majors. Question 4 Select one answer. 10 points A management consultant was interested in whether workers who telecommute are as productive as those who work in the office. She randomly selected 60 workers who were in each of the following three groups: (1) full-time office workers, (2) part-time telecommuters, (3) full time telecommuters. After analyzing the data, the consultant noticed that the variation within groups was large relative to the the variation between sample means. Which of the following is the most correct interpretation of this data? The F statistic will be relatively large, so it is likely that the researcher can conclude that the population means may be equal. The F statistic will be relatively large, so it is likely that the researcher can conclude that the population means are not all equal. The F statistic will be relatively small, so it is likely that the researcher can conclude that the population means may be equal. The F statistic will be relatively small, so it is likely that the researcher can conclude that the population means are not all equal