Final answer:
The statement is true; the Student's t-distribution must be used over the normal distribution for creating confidence intervals when the population standard deviation is unknown, and the sample standard deviation is used as an estimate.
Step-by-step explanation:
The statement is true. When calculating a confidence interval for a mean and the population standard deviation (σ) is unknown, you must use the Student's t-distribution rather than the standard normal (z) distribution. The t-distribution is used because it accounts for the added uncertainty in the estimate of the standard deviation when using the sample standard deviation (s).
The t-distribution is wider than the normal distribution, providing a more conservative and accurate confidence interval when σ is unknown. It's important to note that the sample should be a simple random sample from a population that is approximately normally distributed for the t-distribution to be applicable.
If the sample size is sufficiently large, the central limit theorem ensures that the sampling distribution of the sample mean is approximately normal, and thus the t-distribution can be used even if the population distribution is not known to be normal. This is because the t-distribution becomes closer to the normal distribution as the sample size increases.