Margin of Error Math Example 3

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

Example 3

easy
A 95% CI for average commute time is (28,36)(28, 36) minutes. What is the margin of error, and what does it tell us about the survey's precision?

Solution

  1. 1
    Margin of error: E=36โˆ’282=4E = \frac{36 - 28}{2} = 4 minutes
  2. 2
    The sample mean is xห‰=28+362=32\bar{x} = \frac{28+36}{2} = 32 minutes
  3. 3
    Precision: we can estimate the average commute within ยฑ4 minutes at 95% confidence

Answer

E=4E = 4 minutes. We estimate average commute is 32ยฑ432 \pm 4 min with 95% confidence.
The margin of error directly tells us the precision of our estimate. A ยฑ4 minute margin means we cannot distinguish average commutes that differ by less than 8 minutes. Smaller margins (more precision) require larger samples.

About Margin of Error

The maximum expected difference between the sample statistic and the true population parameter; it is half the width of a confidence interval.

Learn more about Margin of Error โ†’

More Margin of Error Examples

Example 1 easy

A poll of [formula] voters finds [formula] supporting a candidate. Calculate the margin of error at

Example 2 medium

A news report claims: 'The margin of error for this poll is ยฑ3%.' Explain three things a careful rea

Example 4 hard

Two polls: Poll A ([formula]): margin of error ยฑ10%. Poll B ([formula]): margin of error ยฑ2.5%. By w

โ† All Margin of Error Examples Margin of Error Concept