When there is uncertainty about the parameters of a population of interest, a t distribution is used instead of a z distribution.Is the t distribution wider or thinner than the z distribution and why?
A) The t distribution is wider because we are less certain of the findings compared to the z distribution.
B) The t distribution is thinner because we are less certain of the findings compared to the z distribution.
C) They produce the same curve because they both use the population mean.
D) They produce the same curve because they both use the standard deviation of the population.

Question

Quizplus · Accepted Answer

The t distribution is wider because it takes into account the uncertainty of the sample mean due to a smaller sample size and less knowledge about the population standard deviation. This is reflected in the fact that the t distribution has thicker tails than the z distribution.

When There Is Uncertainty About the Parameters of a Population