A quality-control team wants to test whether the average wait time is 6 minutes using a large sample where the population standard deviation is known. Which test is appropriate?

A quality-control team wants to test whether the average wait time is 6 minutes using a large sample where the population standard deviation is known. Which test is appropriate?

• A. One-Sample Z-Test
• B. One-Sample T-Test
• C. Two-Sample T-Test
• D. Matched-Pairs T-Test

Answer: (A)

Testing a single population mean when you know the population standard deviation uses a Z-test for the mean. With a known sigma, the standard normal distribution determines the critical values, and the test statistic is Z = (Xbar − mu0) / (sigma / sqrt(n)). The large sample size supports the normal approximation of the sampling distribution of the mean, making the Z approach appropriate. The one-sample t-test would be used only if sigma were unknown. The two-sample t-test compares two independent means, not a mean against a fixed value. The matched-pairs t-test is for paired measurements, not a single mean against 6.

Testing a single population mean when you know the population standard deviation uses a Z-test for the mean. With a known sigma, the standard normal distribution determines the critical values, and the test statistic is Z = (Xbar − mu0) / (sigma / sqrt(n)). The large sample size supports the normal approximation of the sampling distribution of the mean, making the Z approach appropriate. The one-sample t-test would be used only if sigma were unknown. The two-sample t-test compares two independent means, not a mean against a fixed value. The matched-pairs t-test is for paired measurements, not a single mean against 6.