A z-test for a population mean is used when the population standard deviation σ is known and the sampling distribution of the test statistic can be treated as normal. The test statistic has the form z = (sample statistic − hypothesized parameter) divided by the standard error. Knowing σ allows the standard error to be computed using σ/√n rather than estimating it with the sample standard deviation. Option B describes the common setting for a t-test, not a z-test. Option C is not sufficient by itself; small samples generally require stronger normality assumptions and often favor t-procedures when σ is unknown. Option D is unrelated to the classic z-test for a mean, though z-tests can also be used for proportions under appropriate large-sample conditions. In the provided answer set, the defining condition is that the population standard deviation is known. Study Guide references/topics: z-test, population standard deviation, standard error, hypothesis testing.
