A survey can start with a random sample and still have a response problem. The cue is that households were chosen at random, but only some returned the questionnaire. Compare the group selected with the group that actually supplied data, then ask whether answering could be related to the survey topic. Don't assume random selection makes the respondents unbiased.
Hints
- Hint 1
The target population is the whole group the agency wants to describe. The returned questionnaires describe a smaller group. What would need to be true about that smaller group before its answers could represent all city households?
- Hint 2
Random selection decided who received a questionnaire. Each selected household then decided whether to return it. Does the first decision guarantee that the people who answered represent everyone selected?
- Hint 3
Think about the survey topic: recycling. If people who recycle are more interested in returning this questionnaire, the respondents could differ from households that didn't reply. Can the question tell you whether that happened?
Step-by-step
Check who actually answered
Step 1Identify the group the estimate must describe
No Desmos needed. The issue is who supplied the data, not a percentage calculation. The target population is the group the agency wants to describe: all city households. So the returned questionnaires must represent more than the households that sent them back.
- Step 2
Separate selection from response
The agency randomly selected 500 households to receive the questionnaire, but only 120 returned it. Returning it was the household's decision. Random selection of whom to contact doesn't guarantee a random group of respondents.
- Step 3
Check whether answering could depend on recycling
Of the households that replied, 92 reported recycling. A household that recycles might be more interested in returning a questionnaire about recycling. That's a possible source of nonresponse bias: the people who don't answer may differ in a way that affects the estimate.
- Step 4
Choose the claim the evidence supports
So the low response rate may bias the citywide estimate. We don't know whether recyclers actually replied more often, and we can't determine the city's recycling rate or a definite direction of bias. The claim about what could happen is the one that must be true. Choice C.