Which test is appropriate when the population variance is known and the sample size is large?

• A. T-test.
• B. Nonparametric test.
• C. Chi-square test.
• D. Z-test.

Answer: (D)

If the population variance is known and the sample size is large, you use a Z-test to evaluate a mean. The Z-test relies on the standard normal distribution because the standard error of the sample mean is sigma divided by the square root of n. With a large sample, the sampling distribution of the mean is well approximated by a normal distribution, so you can compute a z statistic as z = (X̄ − μ0) / (σ / √n) and compare it to the standard normal.

The alternative approaches don’t fit these conditions: a t-test is used when the variance is unknown, nonparametric tests don’t assume a specific variance or distribution, and chi-square tests are for testing variances themselves or for relationships like independence, not for testing a mean with known variance.