Question 21 • Probability and Statistics with Applications Honors Sem-1-FL-1210300 (2024-2025)
A new cream was developed to reduce the irritation caused by poison ivy. To test the effectiveness, researchers placed an ad online asking for volunteers to participate in the study. One hundred subjects replied and were informed that one group would receive the new cream and the other would receive a cream with no active ingredient. All 100 subjects were exposed to poison ivy. Fifty were then randomly assigned to the group with the new cream, and 50 were randomly assigned to the group with the cream with no active ingredient. After three days, the subjects’ level of irritation was measured.
Answer
A
The variability between each subject may not be evenly distributed between the two groups, so any observed differences in the level of irritation between the two groups would not be due to the new cream.
B
The variability between each subject would be evenly distributed between the two groups, so any observed differences in the level of irritation between the two groups are more likely due to the new cream.
C
The variability between each type of cream would be evenly distributed between the two groups, so any observed differences in the level of irritation between the two groups are guaranteed to be due to the subjects.
D
The variability between each subject may not be evenly distributed between the two groups, so any observed differences in the level of irritation between the two groups may or may not be due to the new cream.
Explanation
Randomly assigning the 100 subjects to two equal groups helps distribute differences among subjects—such as how sensitive they are to poison ivy—roughly evenly between the groups. This makes the groups comparable, so a difference in irritation is more likely to be caused by the new cream rather than by preexisting differences between subjects. Random assignment does not guarantee an exact balance or prove the cream caused every observed difference.
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