Question

A researcher wanted to know if there is an association between exercise and sleep for the population of 16-year-olds in the United States. She obtained survey responses from a random sample of 2,000 United States 16-year-olds and found convincing evidence of a positive association between exercise and sleep. Which of the following conclusions is well supported by the data?

• A. There is a positive association between exercise and sleep for $16$-year-olds in the United States.
• B. There is a positive association between exercise and sleep for $16$-year-olds in the world.
• C. Using exercise and sleep as defined by the study, an increase in sleep is caused by an increase of exercise for $16$-year-olds in the United States.
• D. Using exercise and sleep as defined by the study, an increase in sleep is caused by an increase of exercise for $16$-year-olds in the world.

Answer 1

The correct option is A There is a positive association between exercise and sleep for $16$-year-olds in the United States.

Choice $A$ is correct. A relationship in the data can only be generalized to the population that the sample was drawn from.

Choice $B$ is not the correct answer. A relationship in the data can only be generalized to the population that the sample was drawn from. The sample was from high school students in the United States, not from high school students in the entire world.

Choice $C$ is not the correct answer. Evidence for a cause-and-effect relationship can only be established when participants are randomly assigned to groups that receive different treatments.

Choice $D$ is not the correct answer. Evidence for a cause-and-effect relationship can only be established when participants are randomly assigned to groups that receive different treatments. Also, a relationship in the data can only be generalized to the population that the sample was drawn from. The sample was from high school students in the United States, not from high school students in the entire world.