Track 8 · Hypothesis Testing · Lesson 6 of 14
Tests for a proportion
Test a claim about a single population proportion with the one-sample z-test or the exact binomial test, and report the result with a confidence interval.
A parcel firm advertises that 90% of deliveries arrive on time. A client checks 400 of its own deliveries and finds 344 on time — 86%. Is that just bad luck in the sample, or evidence that the firm's on-time rate is below its claim? Questions about rates and percentages are among the most common in business, and they have their own tests.
When each observation is a yes/no outcome (on time or late, converted or not, defective or fine), the parameter is a population proportion and the evidence is the sample proportion , where is the number of “successes” among independent trials. Under , the count follows a Binomial(, ) distribution — which gives two ways to test.
Included with a Formula Quest membership
It has 7 graded exercises with feedback, hints and worked solutions. After it you will be able to:
- Compute the one-sample z statistic for a proportion with the null standard error
- Use the exact binomial test when the expected counts are small
- Report a proportion test with the Wilson (or exact) confidence interval
- Check an experiment's traffic split for a sample ratio mismatch