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In: Statistics and Probability

People who eat lots of fruits and vegetables have lower rates of colon cancer than those...

People who eat lots of fruits and vegetables have lower rates of colon cancer than those who eat little of these foods. Fruits and vegetables are rich in "antioxidants" such as vitamins A, C, and E. Will taking antioxidants help prevent colon cancer? A medical experiment studied this question with 864 people who were at risk of colon cancer. The subjects were divided into four groups: daily beta-carotene, daily vitamins C and E, all three vitamins every day, or daily placebo. After four years, the researchers were surprised to find no significant difference in colon cancer among the groups.

Outline the design of the experiment. Use your judgment in choosing the group sizes. (Select all that apply.)

Randomly assign 2 treatments to 4 groups.

Randomly assign subjects to 4 treatments.

Observe the occurrence of colon cancer.

Randomly assign subjects to 2 treatments.

Observe eating habits.

Suggest some possible reasons (lurking variables) that could explain why people who eat lots of fruits and vegetables have lower rates of colon cancer. The experiment suggests that these variables, rather than the antioxidants, may be responsible for the observed benefits of fruits and vegetables. (Select all that apply.)

People who eat lots of fruits and vegetables may have healthier diets overall.
People who eat more fruits and vegetables may exercise more.
People who eat lots of fruits and vegetables may watch more TV.
Fruits and vegetables contain fiber and this could account for the benefits of those foods.
Fruits and vegetables do not contain any sugar and this could account for the benefits of those foods.

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