A survey asking for the most appropriate inference tests how far its result can be generalized. Find the group the random sample came from: the result can support an estimate for that group, not automatically for a larger one. Then check whether the percentage supports a majority claim, and reject any claim of cause and effect that the survey didn't test.
Hints
- Hint 1
In random sampling, chance selects people from a specified group. Look at who was eligible for the survey, not only at the word randomly. Could every city resident have been chosen?
- Hint 2
A majority means more than half. Compare the support percentage with , then keep the conclusion within the group that was sampled.
Step-by-step
Match the inference to the sampled group
Step 1Find who could have been chosen
No Desmos needed. The decision is about who could be sampled, not a calculation. The sample is the residents surveyed. They were chosen at random only from residents who commute by bicycle at least twice a week. So random sampling supports an inference about the group sampled, not everyone in the city.
- Step 2
Interpret the support percentage
A majority means more than half. Since is greater than , most people surveyed supported the lanes. Their percentage supports an estimate for the biking group they were randomly picked from; it isn't an exact count of that whole group's opinions.
- Step 3
Choose the claim the survey supports
The survey asked about support, not what would happen after lanes were added, so it doesn't show cause and effect. The supported inference is that most residents who commute by bicycle at least twice a week would support adding protected bike lanes downtown. Choice C.