Which of the following statements are TRUE?
(A) The variable t of t-distribution ranges from $-∞$ to $∞$.
(B) The probability curve of the t-distribution is symmetric about the line $t=0$
(C) The variance of the t-distribution is greater than one.
(D) As the number of degrees of freedom decreases, the t-distribution curve moves closer to the standard normal probability curve.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A), (B) and (C) only **
(A) True. The t-statistic ranges over the entire real line: $(-\infty,\infty)$.
(B) True. The t-distribution is symmetric about $t=0$.
(C) True for all degrees of freedom $v>2$. Variance of t-distribution is $\frac{v}{v-2}$, which is always greater than 1.
(D) False. As degrees of freedom increase, the t-distribution approaches the standard normal curve. If degrees of freedom decrease, it becomes wider, not closer.
Correct statements: (A), (B), (C)