Question

question 1
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
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?
a. yes, because 6.17 - 4.78 < 2.
b. yes, because 6.17/4.78 < 2.
c. no, because the standard deviations are not equal.

Explanation:

Step1: Recall ANOVA condition

One of the assumptions for ANOVA is that the population standard - deviations are equal. A rule - of - thumb is that if the ratio of the largest sample standard deviation to the smallest sample standard deviation is less than 2, the equal - variance assumption is considered met.

Step2: Identify largest and smallest s.d.

The largest sample standard deviation is $s_{max}=6.1661669$ (Social Sciences) and the smallest is $s_{min}=4.7821787$ (Math).

Step3: Calculate the ratio

Calculate the ratio $\frac{s_{max}}{s_{min}}=\frac{6.1661669}{4.7821787}\approx1.29$. Since $1.29 < 2$, the data meet the equal - variance condition for ANOVA.

Answer:

B. Yes, because 6.17/4.78 < 2.