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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.Here are the three sample standard deviations for the MCAT scores for the three groups (biological sciences majors, social sciences majors, math majors):Column Std. HeadBiological Sciences 5.3115216Social Sciences 6.1661669Math 4.7821787Based on this information, do the data meet the condition of equal population standard deviations for the use of the ANOVA? Yes, because 6.17 − 4.78 < 2. Yes, because 6.17/4.78 < 2. No, because the standard deviations are not equal.

Question

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.Here are the three sample standard deviations for the MCAT scores for the three groups (biological sciences majors, social sciences majors, math majors):Column Std. HeadBiological Sciences 5.3115216Social Sciences 6.1661669Math 4.7821787Based on this information, do the data meet the condition of equal population standard deviations for the use of the ANOVA? Yes, because 6.17 − 4.78 < 2. Yes, because 6.17/4.78 < 2. No, because the standard deviations are not equal.

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Solution

The condition for using ANOVA (Analysis of Variance) is that the populations from which the samples are drawn have equal standard deviations. This condition is known as the assumption of homogeneity of variances.

To check this condition, we often use Levene's test or Bartlett's test. However, in the absence of these tests, a common rule of thumb is that the ratio of the largest standard deviation to the smallest standard deviation should not be greater than 2.

In this case, the largest standard deviation is 6.1661669 (Social Sciences) and the smallest is 4.7821787 (Math).

So, we calculate the ratio: 6.1661669 / 4.7821787 = 1.29 (approximately)

Since 1.29 is less than 2, we can say that the data meet the condition of equal population standard deviations for the use of ANOVA.

So, the correct answer is: "Yes, because 6.17/4.78 < 2."

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Similar Questions

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