When is the one sample t-test used?

The one sample t-test is specifically used when you want to compare the sample mean of a population to a known value (often the population mean or a theoretical value) and when the population standard deviation is not known. This situation often arises in practical scenarios where researchers work with sample data rather than population data and do not have the exact population parameters for the standard deviation.

In instances where the population standard deviation is unknown, the t-test becomes necessary because it allows for estimating the population variance from the sample data. This statistical test adjusts for the added uncertainty that comes with estimating population parameters from a smaller sample, which is particularly important when the sample size is small (generally less than 30).

In contrast, if the population mean is known, a different test, such as a z-test, might be more appropriate if the population standard deviation is also known. As for the sample size, while a larger sample size (typically 30 or more) allows the t-distribution to approximate the normal distribution, it is not a requirement for conducting a one sample t-test as it can still be employed for smaller sample sizes, provided the standard deviation is unknown.

Therefore, option B provides the necessary condition under which the one sample t-test is appropriately