09 / 12 · Learn from a sample
An estimate is not an exact address
Read a confidence interval without mistaking it for the spread of individual answers.
Builds on Why does a small sample jump around?
Go to practice ↓A question to keep in mind
A survey gives a 95% confidence interval from 44% to 56%. What does the 95% describe?
A sample gives an estimate of a population value, such as the share of all readers who prefer evening hours. A confidence interval adds a range to express uncertainty in that estimate. It is not a range containing 95% of individual answers.
If the sampling and calculation conditions hold, repeating a 95% interval method would cover the true value about 95% of the time in the long run. A particular interval either covers it or misses it. Any one set of 100 intervals need not contain exactly 95 hits.
Work through an example
- Interval A runs from 44% to 56%, a width of 12 percentage points.
- If the true population value in a teaching example were 50%, A and B would cover it, while C would not.
- In a real survey we usually do not know that true value; that is why we estimate it.
Your turn
0 / 3For interval A, from 44% to 56%, what is its width in percentage points?
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- Interval width: 12 points
The width is 56 - 44 = 12 percentage points. This is a width, not a claim that 12% of people are uncertain.
What is the intended meaning of a 95% confidence-interval method when its conditions hold?
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Across repeated uses, about 95% of the intervals would cover the true quantity in the long run.
Think of a method producing many intervals. Some miss. The stated rate is a long-run coverage property, conditional on the method's assumptions.
You repeat a valid 95% interval method 100 times. Must exactly 95 intervals cover the true value?
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No. That particular batch can have more or fewer hits.
The same lesson returns: a probability or coverage rate is not a guaranteed schedule for a short run.
Bring it back to your own work
Write a two-sentence explanation of a confidence interval for someone who has never studied statistics. Include what it does not describe.
Statistical literacy: directory, audit and transfer assessment
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