When using the Student's $t$ distribution to construct a confidence interval for the population mean, which of the following conditions must be met?

• A. The population standard deviation is known and the sample size is always greater than $30$.
• B. The population standard deviation is unknown and the sample is drawn from a normally distributed population.
• C. The sample size must be less than $10$.
• D. The sample is always drawn from a population with a mean of zero.

Answer: (B)

Verified step by step guidance

1. Understand that the Student's t distribution is used when the population standard deviation is unknown and the sample size is relatively small or the population distribution is normal.
2. Recall that the t distribution is appropriate when the sample is drawn from a population that is approximately normally distributed, especially for small sample sizes.
3. Note that the population standard deviation being known typically leads to using the normal (Z) distribution, not the t distribution.
4. Recognize that the sample size does not have to be greater than 30 for the t distribution; in fact, the t distribution is often used when the sample size is less than 30.
5. Understand that the population mean does not have to be zero for the t distribution to be applicable; the mean can be any value.