Which statement correctly compares t-distributions to the Normal distribution?
I. t distributions are also mound shaped and symmetric.
II. t distributions are more spread out than the normal distribution.
III. As degrees of freedom increase, the variance of t distributions becomes larger.
A) I and III only
B) II only
C) I, II, and III
D) I and II only
E) I only

Question

Quizplus · Accepted Answer

Statement I is true, as t-distributions and the Normal distribution are both mound shaped and symmetric. 
Statement II is also true, as t-distributions have more spread (larger variance) than the Normal distribution. 
However, Statement III is false. As degrees of freedom increase, the variance of t-distributions decreases, approaching the variance of the Normal distribution. Therefore, choice D is the best answer as it correctly includes the true statements (I and II) while excluding the false statement (III).

Which Statement Correctly Compares T-Distributions to the Normal Distribution