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. let $mu_1$, $mu_2$, and $mu_3$ 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? a. $h_0:mu_1=mu_2=mu_3$ $h_a:mu_1,mu_2,mu_3$ are not all equal b. $h_0:mu_1,mu_2,mu_3$ are not all equal $h_a:mu_1=mu_2=mu_3$ c. $h_0:mu_1=mu_2=mu_3$ $h_a:mu_1
eqmu_2
eqmu_3$ d. $h_0:mu_1
eqmu_2
eqmu_3$ $h_a:mu_1=mu_2=mu_3$ question 3

Explanation:

Step1: Define null and alternative hypotheses

The null hypothesis ($H_0$) in an ANOVA - type situation (comparing means of multiple groups) is that all population means are equal. The alternative hypothesis ($H_a$) is that not all population means are equal.

Step2: Analyze options

In this case, we are comparing the MCAT scores of three groups (biological sciences majors, social science majors, and math majors) with population means $\mu_1$, $\mu_2$, and $\mu_3$. The null hypothesis should be $H_0:\mu_1=\mu_2=\mu_3$ and the alternative hypothesis should be $H_a:\mu_1,\mu_2,\mu_3$ are not all equal.

Answer:

A. $H_0:\mu_1 = \mu_2=\mu_3$; $H_a:\mu_1,\mu_2,\mu_3$ are not all equal