MCAT Math Question 34: Answer and Explanation
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Question: 34
4. A hypothesis test was correctly conducted and the experimenter failed to reject the null hypothesis. Which of the following must be true?
I. The p-value was greater than α.
II. A type I error did not occur.
III. The power of the study was too small.
- A. I only
- B. II only
- C. I and II only
- D. I and III only
Correct Answer: B
Explanation:
A type I error occurs when the null hypothesis is incorrectly rejected. Because we failed to reject the null hypothesis, this could not have occurred. Statement I is incorrect because in a two-sided test, the p-value only needs to exceed
Statement III is incorrect because we lack information about power in the question stem. In addition, a study could be extremely well-powered and still fail to reject the null hypothesis if no difference truly exists between two populations.