Margin of Error Statistics Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

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

Solution

  1. 1
    Step 1: Margin of error is proportional to 1n\frac{1}{\sqrt{n}}.
  2. 2
    Step 2: If nn is quadrupled (×4), then n\sqrt{n} doubles, so the margin of error is halved.
  3. 3
    Step 3: For example, if ME = 6% with n=100n = 100, then with n=400n = 400, ME ≈ 3%.

Answer

Quadrupling the sample size halves the margin of error.
There are diminishing returns to increasing sample size. To halve the margin of error, you need four times as many observations. This guides practical decisions about study design.

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 1 hard

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

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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