Question 7 • Probability and Statistics with Applications Honors Sem-2-FL-1210300 (2024-2025)
A drug manufacturing company believes it has found a new medication to alleviate pain for headache sufferers. Twenty people with chronic headaches are asked to take a placebo pill or a pill containing the new medication during their next headache episode. The pill they take is determined by a coin flip. An hour later, the participants are asked to rate their headache pain level on a scale from 1 (no pain) to 5 (severe pain). During their next headache episode, the subjects are asked to take the other pill. The difference in pain ratings (new pill – placebo) is calculated for each subject. Are the conditions for inference met?
Answer
A
No. The random condition is not met.
B
No. The 10% condition is not met.
C
No. The Normal/Large Counts condition is not met because the sample size is too small and the shape of the distribution of differences is not known.
D
Yes. All conditions are met.
Explanation
The coin flip randomizes which pill is taken first, and the same 20 people try both pills, so the comparison is paired. The 10% condition is reasonable for a group of 20 headache sufferers. However, there are only 20 paired differences, and the question gives no information about their distribution. With a small sample, we cannot assume the differences are approximately Normal, so the Normal/Large Counts condition is not established.
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