SAT OwlQuestion bank / Evaluating statistical claims: observational studies and experiments
A city mailed a survey about a proposed dog park to randomly selected households. Only households returned the survey, and of them opposed the dog park. A council member concludes that about of all households in the city oppose the dog park. Which of the following is the best evaluation of this conclusion?
It is justified, because the households were selected at random.
It is justified, because responses is a large enough sample.
It is not justified, because of is only households, which is far fewer than half of .
It is not justified, because the households that chose to return the survey may differ in their opinions from the households that did not.
Show answer and explanation
Answer: D
The city selected households at random, but only of them responded. Households with strong opinions, such as those who oppose the park, may be more likely to return a survey. Because the households decided for themselves whether to respond, the respondents may not represent all households.
Choice A is tempting, but random selection prevents bias only if nearly every selected household responds, and here most didn't.
Why the other choices are wrong
- A. Random selection helps only if most selected households respond, and only 13% did.
- B. A sample of 260 can be enough, but not when the respondents chose themselves.
- C. This confuses a count with a percent; the problem is nonresponse, not the number 208.
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