A margin of error for a survey percentage tells you how far on either side of the estimate to look for the population percentage. Subtract and add the margin in percentage points, then check that the conclusion describes the group sampled at random. The range supports a high-confidence estimate, not a guarantee about the true value or a claim about whether respondents answered honestly.
Hints
- Hint 1
A sample is the group surveyed; the population is the larger group the researcher wants to describe. The freshmen were randomly selected from the state. Is the margin about their individual answers or the statewide percentage?
- Hint 2
A margin of error goes on both sides of an estimate. Add and subtract it as percentage points, rather than taking a percent of the estimate. What are the two endpoints around ?
Step-by-step
Build and interpret the margin-of-error interval
Step 1Identify whose percent is estimated
No Desmos needed. The estimate is given, and each endpoint takes one operation. The freshmen surveyed are the sample, the people actually asked. All college freshmen in the state are the population, the larger group the researcher wants to describe. So the reported estimates a statewide percentage.
- Step 2
Read the margin as a distance
A margin of error gives a range around the estimate: . Here the margin means percentage points on either side of , not of . It measures uncertainty in the statewide estimate, not whether anyone answered falsely.
- Step 3
Find the lower endpoint
Subtract the margin to get the lower end of the range:
- Step 4
Find the upper endpoint
Add the same margin to get the upper end:
- Step 5
Choose the claim the interval supports
Because the freshmen were randomly selected, the interval supports an estimate for all college freshmen in the state. High confidence is not certainty: a true percentage outside the interval is possible. So, with high confidence, the statewide percentage who worked full-time is between and . Choice C.