Final answer:
Use a t-distribution when testing a null hypothesis about a single population mean with an unknown population standard deviation, employing the sample standard deviation as an estimate.
Step-by-step explanation:
When testing a null hypothesis about a single population mean and the population standard deviation is unknown, the appropriate distribution to use is the t-distribution. This decision is based on the fact that the sample standard deviation is used as an estimate for the unknown population standard deviation. The Student's t-distribution is utilized under the conditions that the data is a simple random sample from a population that is approximately normally distributed, or if the sample size is large enough. Moreover, when the population variance is unknown and the sample size is small, as in the case where the sample size is 10 and the population is normal, a t-test is also used, with the degrees of freedom calculated as the sample size minus one.