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 open paren new pill minus placebo close paren is calculated for each subject. Are the conditions for inference met?
Answer
A
No. The 10 percent condition is not met.
B
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.
C
Yes. All conditions are met.
D
No. The random condition is not met.
Explanation
This is a paired study, so inference uses the 20 differences in pain ratings (new pill minus placebo). With only 20 differences, the sample is not large enough by itself to guarantee an approximately Normal sampling distribution, and the question gives no information about the shape of the differences. Therefore, the Normal/Large Counts condition cannot be confirmed. The correct choice is B: the sample is too small and the shape of the distribution of differences is unknown.
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