In interval estimation, the t distribution is applicable only when the
A) population has a mean of less than 30.
B) sample standard deviation is used to estimate the population standard deviation.
C) variance of the population is known.
D) mean of the population is unknown.

Question

Quizplus · Accepted Answer

The t distribution is used for interval estimation when the sample standard deviation is used to estimate the population standard deviation. This is because when the population standard deviation is unknown, the sample standard deviation is used as an estimate, and the t distribution adjusts for the increased uncertainty introduced by using an estimate rather than a known value. The other options (A, C, and D) are incorrect because they either limit the applicability of the t distribution unnecessarily or do not address the key factor of using a sample standard deviation to estimate the population standard deviation.

In Interval Estimation, the T Distribution Is Applicable Only When