Q. AP4.26 Which of the following statement... [FREE SOLUTION]

91影视

The Practice of Statistics for AP Examination

Daren Starnes, Josh Tabor

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 837 pages

ISBN: 9781319113339

Chapter 12: Q. AP4.26 (page 831)

Which of the following statements about the t distribution with degrees of freedom $d f$ is (are) true?
I. It is symmetric.
II. It has more variability than the t distribution with $d f + 1$ 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

Expert verified

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.