Track 7 · Estimation and Confidence Intervals · Lesson 6 of 10
Interval for a proportion
Build Wald and Wilson intervals for a proportion, and recognise when the Wald interval fails.
A screening test detected the condition in 90 of the 93 people who truly had it. A textbook formula gives a 95% interval for the test's sensitivity that reaches above 100% — an impossible value. The fault is the formula, not the data, and a better interval is just as easy to compute.
A proportion — the share of customers who renew, of patients who respond, of parts that are defective — is estimated by , the number of successes over the number of trials. Its standard error is , and since is unknown the simplest interval plugs in .
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It has 7 graded exercises with feedback, hints and worked solutions. After it you will be able to:
- Compute the Wald and Wilson intervals for a proportion
- Recognise the Wald interval's failures: zero width, impossible bounds, low coverage
- Choose Wilson by default, especially for small counts or proportions near 0 or 1
- Interpret coverage as the long-run success rate of an interval method