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. Head Biological Sciences 5.3115216 Social Sciences 6.1661669 Math 4.7821787 Based 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.

Answer 1

Yes, because 6.17/4.78 < 2

Explanation:

To test for equal standard deviation ;

Condition is met if the ratio of the large sample standard deviation to the smaer sample standard deviation is less than 2

Sample standard deviation;

Sciences 6.1661669

Math 4.7821787

Biological Sciences 5.3115216

The largest sample standard deviation = 6.1661669

The smallest sample standard deviation = 4.7821787

F statistic = 6.1661669 / 4.7821787 = 1.2894053

F statistic < 2 ; Hence, condition for equal standard deviation is met.