Question

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 $df+1$degrees of freedom. III. III. As df increases, the t distribution approaches the standard Normal distribution.

a. I only

b. II only

c. III only

d. I and III

e. I, II, and III

Short answer

The correct answer is option (e) I, II, and III.

Step-by-step solution

Concept introduction

In quantitative tests, segmentation is the technique of selecting a predefined dataset from a huge population. Vary based on the type of assessment being undertaken, the measures taken to recruit from a general community may include simple chance picking or standard normal distribution.

Explanation

Three statements are offered in the question. The true statement for degrees of freedom must be discovered. As a result, based on the statements, we may conclude that

Because all $t-$distributions are symmetric, the first statement is correct. Because the degrees of freedom decrease, the $t-$distribution becomes broader, and hence the $t-$distribution has greater variability, the second assertion is correct. It is true in the third assertion because the $t$distribution closely mimics the conventional normal distribution as the degrees of freedom increase. As a result, option (e) is the proper choice.