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. the following hypotheses were tested: h₀:μ₁ = μ₂ = μ₃ hₐ:μ₁,μ₂,μ₃ are not all equal the analysis was run on the data and the following output was obtained: anova table 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 4670.1672 which of the following is an appropriate conclusion based on the output? 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 students major and mcat score. c. reject h₀ and conclude that the data provide strong evidence that there is a relationship between the students 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. question 4 a management consultant was interested in whether workers who telecommute are as productive as those who work in the office. she randomly selected 60 workers who were in each of the following three groups: (1) full - time office workers, (2) part - time telecommuters, (3) full time telecommuters. after analyzing the data, the consultant noticed that the variation within groups was large relative to the the variation between sample means. which of the following is the most correct interpretation of this data?

Explanation:

Step1: Recall hypothesis - testing decision rule

In hypothesis - testing, if the p - value is less than the significance level (commonly $\alpha = 0.05$), we reject the null hypothesis $H_0$.

Step2: Identify the p - value

From the ANOVA table, the p - value is $0.0071$. Since $0.0071<0.05$.

Step3: Make a conclusion

We reject the null hypothesis $H_0:\mu_1=\mu_2=\mu_3$. Rejecting $H_0$ means there is strong evidence that there is a relationship between the student's major and MCAT score.

Answer:

C. Reject $H_0$ and conclude that the data provide strong evidence that there is a relationship between the student's major and MCAT score.