Practice Margin of Error in Statistics

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

The margin of error is the maximum expected difference between a sample statistic and the true population parameter, typically expressed as a plus-or-minus value. It equals half the width of a confidence interval and decreases as sample size increases.

When a poll says '52% \pm 3%,' that 3% is the margin of error. It means the true value is probably within 3 percentage points of 52%, so between 49% and 55%.

Example 1

hard
A poll of 400 voters found 55% support a policy. Calculate the margin of error for a 95% confidence interval.

Example 2

hard
How does quadrupling the sample size affect the margin of error?

Example 3

hard
A 95% CI for a mean is 50 \pm 3. What is the margin of error, and what would it be if the sample size were quadrupled?

Example 4

hard
If the confidence level is increased from 90% to 99% while the sample size and variability stay the same, what happens to the margin of error?
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