One-proportion z-test
A one-proportion z-test checks whether a population proportion equals a claimed value by comparing the sample proportion to that claim using the normal approximation, producing a z-statistic to judge the gap.
See it move
A subscription service claims at least 60% of customers renew. A sample of 150 customers shows 99 renewals, a sample proportion of 66%. Using the claimed 60% to build a standard error of 0.04, the z-statistic is (0.66 − 0.60) ÷ 0.04 = 1.5. That falls short of the 1.645 critical value at 5% significance, so the evidence isn't strong enough to confirm the claim.
The formula
Variables
- Sample proportion
- Hypothesised (claimed) population proportion
- Sample size (count)
Standardises the gap between the observed sample proportion and the hypothesised population proportion so it can be compared against the standard normal distribution.
Check yourself
A logistics company claims that at least 80% of its shipments arrive on time (p0 = 0.80). A random sample of 100 shipments finds that 72 arrived on time (p̂ = 0.72). What is the z-statistic for testing this claim?