Final answer:
The Student's t-distribution should be used for setting confidence intervals when the sample size is small and the population variance is small or unknown. The correct answer is C.
Step-by-step explanation:
When setting a confidence interval for the population mean of a normal or approximately normal distribution with a small sample size, the correct approach is to use the Student's t-distribution when the variance is small or unknown.
The Student's t-distribution is especially important in cases where the population standard deviation (o) is not known and the sample standard deviation (s) is used as an estimate. Using t-distribution is crucial because the normal distribution, while accurate when the population standard deviation is known, does not yield as accurate results when working with an estimate based on the sample.
Furthermore, the assumption that the population is normally distributed or the sample size is large enough validates the use of the t-distribution. The t-distribution provides a more accurate estimate of the population parameters under these conditions, particularly when dealing with small sample sizes. It is essential to understand that the Student's t-distribution becomes closer to the normal distribution as the sample size increases and the degrees of freedom grow.