1. Let's state the problem: We want to know when a researcher should use a one-sample t-test instead of a z-test. 2. A one-sample z-test is typically used when the population mean and population standard deviation (variability) are known, and the sample size is large (usually greater than 30). 3. A one-sample t-test is used when the population variability (standard deviation) is unknown, which is often the case in real-life situations, and especially with smaller sample sizes. 4. Now, let's analyze the options: - "When the sample is greater than 30": Large samples often justify the use of z-test, not necessarily t-test. - "When the population mean is unknown": The population mean is usually unknown for both tests; this is not the deciding factor. - "When comparing two groups": This is about two-sample tests, not one-sample tests. - "When the population variability is unknown": This is the key condition for using a one-sample t-test. 5. Conclusion: A one-sample t-test should be used when the population variability is unknown.