Margin of Error Statistics Example 1

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Example 1

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

Solution

  1. 1
    Step 1: For proportions, SE=p^(1−p^)n=0.55×0.45400=0.2475400=0.000619≈0.0249\text{SE} = \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} = \sqrt{\frac{0.55 \times 0.45}{400}} = \sqrt{\frac{0.2475}{400}} = \sqrt{0.000619} \approx 0.0249.
  2. 2
    Step 2: Margin of error = z∗×SE=1.96×0.0249≈0.049z^* \times \text{SE} = 1.96 \times 0.0249 \approx 0.049.
  3. 3
    Step 3: The margin of error is approximately ±4.9 percentage points.

Answer

Margin of error ≈ ±4.9 percentage points.
The margin of error quantifies the precision of an estimate. A smaller margin means a more precise estimate. Increasing sample size reduces the margin of error.

About Margin of Error

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.

Learn more about Margin of Error →

More Margin of Error Examples

Example 2 hard

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

Example 3 hard

A 95% CI for a mean is [formula]. What is the margin of error, and what would it be if the sample si

Example 4 hard

If the confidence level is increased from 90% to 99% while the sample size and variability stay the

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