When constructing a confidence interval for a population mean,if a population is normally distributed and a small sample is taken,then the distribution of $\bar { X }$
Is based on the ____________ distribution.
A)z
B)t
C)Neither
D)Both z and t

Question

Quizplus · Accepted Answer

If the population is normally distributed and a small sample is taken, then the sample mean $\bar{X}$ follows the t-distribution. The z-distribution is only used if the population standard deviation is known or if the sample size is large (usually n > 30). Therefore, in this scenario, the t-distribution is the appropriate choice to construct the confidence interval for the population mean.

When Constructing a Confidence Interval for a Population Mean,if a Population