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Chapter 12: Q. AP4.26. (page 803)

Which of the following statements about the t distribution with degrees of freedom df is (are) true?

I. It is symmetric.

II. It has more variability than the t distribution with df+1degrees of freedom.

III. As df increases, the t distribution approaches the standard Normal distribution.

(a) I only (c) III only (e) I, II, and III

(b) II only (d) I and II

Short Answer

Expert verified

(e) I, II and III are true.

Step by step solution

01

Given information

we have been given that

tdistribution with degree of freedom df

02

Explanation

I:True, because all t-distributions are symmetric.

II:True, because as the degree of freedom decreases, the t-distribution becomes wider and thus the t-distribution has more variability (when it has a lower degrees of freedom).

III:True, because the larger the degree of freedom, the more closely the t-distribution resembles the standard Normal distribution.

Since, I,IIandIIIare all correct, the correct answer option is(e)I,IIandIII

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