A margin of error gives a plausible range around a survey percentage. Add and subtract percentage points, not a percent of the estimate. Check that the random sample came from the group named in the claim. To support a claim that more than half favor something, the range’s lower endpoint must exceed . A survey estimate cannot prove an exact population percentage.
Hints
- Hint 1
A random sample uses chance to select people from a larger group. Since the people sampled are adult county residents, the survey can provide evidence about all adult county residents, even without asking every one of them.
- Hint 2
A margin of error of percentage points means go points below and points above the reported . Don’t take of . What are the two endpoints?
- Hint 3
To judge a claim about more than half, compare with the lower endpoint, the smallest plausible population percentage. If even that endpoint is above , what does the survey support?
Step-by-step
Build the plausible range
Step 1Identify the group the survey can describe
A random sample uses chance to pick people from a larger group. The people were sampled from adult county residents, so the survey can support an estimate for that same group. It doesn’t have to ask every adult.
- Step 2
Find the lower endpoint
The margin of error says the population percentage could plausibly be percentage points below the sample’s . Type in Desmos; it displays , so the lower endpoint is . Subtract points, not of .
- Step 3
Find the upper endpoint
The margin also reaches points above . Type on the next Desmos line; it displays , so the upper endpoint is . The plausible range is to .
- Step 4
Compare the range with half
Even the lowest plausible percentage, , is above . So the survey supports the conclusion that more than half of adult county residents favor extending weekend hours. It does not prove their exact percentage. Choice A.