Statistics

Confidence Intervals: What They Really Mean

Learn how to build and correctly interpret a confidence interval with two worked examples.

The setup

The 95% describes the method, not one interval: it captures the true value in about 95% of repeated samples.

Example 1

A sample gives x̄ = 50 with margin of error 4. Find the 95% interval.

  1. Lower = 50 − 4 = 46
  2. Upper = 50 + 4 = 54
(46, 54)

Example 2

How do you interpret (46, 54) at 95% confidence?

  1. Say: we are 95% confident the true mean is between 46 and 54
  2. The true mean is a fixed number, not random
95% confident the mean is in (46, 54)

Common mistake

There is a 95% probability the true mean is in (46, 54)

Once computed, the interval either contains the true mean or it doesn't.

A larger sample or lower confidence level gives a narrower interval.

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