A margin of error describes uncertainty from random sampling. To compare two surveys, first check whether their sample sizes and confidence levels differ. If those factors are fixed, compare the estimated percentages: yes-or-no results vary most across random samples when responses are close to an even split, not merely when the reported percentage is larger.
Hints
- Hint 1
A confidence level sets how certain the margin-of-error calculation aims to be. Both surveys use the same confidence level and sample size. Can either of those factors explain why their margins differ?
- Hint 2
A sample proportion is the fraction of surveyed people who give a particular answer. To compare the estimates, consider both the yes and no shares in each sample. How do those pairs of shares differ?
Step-by-step
Compare how close the estimates are to half
Step 1Rule out the factors held fixed
No Desmos needed. The table and a property of sample proportions settle this comparison without a calculation. Both samples have 900 voters, and both margins use a confidence level. So neither sample size nor confidence level explains why one margin is greater.
- Step 2
Connect the estimate to sampling variability
Sampling variability means how much an estimated percentage can change when you choose a different random sample. For a yes-or-no question, a result near half yes and half no varies most. With sample size and confidence level fixed, an estimate nearer has a greater margin of error.
- Step 3
Compare the two sample percentages
Sample D's is much closer to than sample C's . So D has greater sampling variability, which explains its greater margin of error. Choice B.