Which of the characteristics below distinguishes the t statistic from the z statistic?
A) the proportion of area beyond a particular positive t value is equal to the proportion of area below the corresponding negative t
B) the z distribution has a mean of zero while the t distribution does not
C) In the t distribution the area under the curve beyond a value of ±1.96 is greater than that of the normal curve
D) all of these

Question

Quizplus · Accepted Answer

The t distribution is more spread out and has heavier tails than the normal distribution, meaning that for the same value (e.g., ±1.96), there is more area beyond that value in the t distribution compared to the normal (z) distribution. This accounts for the increased uncertainty (due to estimating the population standard deviation with the sample standard deviation) when using the t distribution.

Which of the Characteristics Below Distinguishes the T Statistic from the Z