Practice Margin of Error in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
The maximum expected difference between the sample statistic and the true population parameter; it is half the width of a confidence interval.
When a poll says 'the approval rating is 52\% with a margin of error of \pm 3\%,' it means the true value is likely between 49\% and 55\%. The margin of error is the '\pm' part—it tells you how much wiggle room to give the estimate. Larger samples and less variability shrink the margin of error.
Example 1
easyA poll of n=400 voters finds \hat{p}=0.55 supporting a candidate. Calculate the margin of error at 95% confidence and interpret the result.
Example 2
mediumA news report claims: 'The margin of error for this poll is ±3%.' Explain three things a careful reader should know about this margin of error.
Example 3
easyA 95% CI for average commute time is (28, 36) minutes. What is the margin of error, and what does it tell us about the survey's precision?
Example 4
hardTwo polls: Poll A (n=100): margin of error ±10%. Poll B (n=1600): margin of error ±2.5%. By what factor was n increased, and by what factor did E decrease? Verify using E = z^* \sqrt{\frac{0.5 \times 0.5}{n}}.