2. A medical school admissions officer was interested in whether there is a diff
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2. 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 µ1, µ2, and µ3 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?
A: H0: 1 = 2 = 3 Ha: 1, 2, 3, are not all equal
B: H0: 1, 2, 3, are not all equal Ha: 1 = 2 = 3
C: H0: 1 = 2 = 3 Ha: 1 2 3
D: H0: 1 2 3 Ha: 1 = 2 = 3
3. 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
A: 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.
B: 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.
C: Reject H0 and conclude that the data provide strong evidence that there is a relationship between the student’s major and MCAT score.
D: 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.
4. A psychology program coordinator was interested in whether there was a difference in salary for the mental health counseling graduates of her master’s degree program based on whether they obtained employment in (1) a sole proprietor private practice, (2) a group private practice, (3) hospitals or (4) government agencies. After analyzing the data for 90 recent graduates, the consultant noticed that the variation within groups was small relative to the the variation between sample means. Which of the following is the most correct interpretation of this data?
A: The F statistic will be relatively large, so it is likely that the researcher can conclude that the population means may be equal.
B: The F statistic will be relatively large, so it is likely that the researcher can conclude that the population means are not all equal.
C: The F statistic will be relatively small, so it is likely that the researcher can conclude that the population means may be equal.
D: The F statistic will be relatively small, so it is likely that the researcher can conclude that the population means are not all equal. pg. 252
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 4670.1672Explanation / Answer
2) option A and C are approriate with respect to Null and alternative hypothesis
3) Since turkey post hoc results were not given we choose option C: Reject H0 and conclude that the data provide strong evidence that there is a relationship between the student’s major and MCAT score.
4) B: The F statistic will be relatively large, so it is likely that the researcher can conclude that the population means are not all equal.
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