i. The t distribution is positively skewed. ii. All t distributions have the same mean of zero and a standard deviation of 1.
iii. The t distribution is more spread out and flatter at the center than is the standard normal distribution. However, as the sample size increases, the t distribution curve approaches the standard normal distribution.
A) (i), (ii), and (iii) are all correct statements.
B) (iii) is a correct statement but not (i) or (ii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question

Quizplus · Accepted Answer

- The t distribution is symmetric and not positively skewed, so (i) is incorrect.- The t distribution does have a mean of zero, but its standard deviation is not 1; it varies depending on the degrees of freedom, so (ii) is incorrect.- Statement (iii) is correct; the t distribution is indeed more spread out and flatter at the center compared to the standard normal distribution, and it does approach the standard normal distribution as the sample size (and thus degrees of freedom) increases.

I the T Distribution Is Positively Skewed