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Introductory Statistics

Neil A. Weiss

Chapter 13

Chi-Square Procedures - all with Video Answers

Educators

Section 1

The Chi-Square Distribution

01:13

Problem 1

Understanding the Concepts and Skills
What is meant by saying that a variable has a chi-square distribution?

Tyler Moulton
Tyler Moulton
Numerade Educator
01:02

Problem 2

How do you identify different chi-square distributions?

Tyler Moulton
Tyler Moulton
Numerade Educator
01:04

Problem 3

Consider two $x^{2}$ -curves with degrees of freedom 12 and 20 respectively. Which one more closely resembles a normal curve? Explain your answer.

Tyler Moulton
Tyler Moulton
Numerade Educator
00:39

Problem 4

The $t$ -table has entries for areas of 0.10,0.05,0.025,0.01 and $0.005 .$ In contrast, the $x^{2}$ -table has entries for those areas and for $0.995,0.99,0.975,0.95,$ and $0.90 .$ Explain why the $t$ -values corresponding to these additional areas can be obtained from the existing $t$ -table but must be provided explicitly in the $x^{2}$ -table.

Maxime Rossetti
Maxime Rossetti
Numerade Educator
01:02

Problem 5

Use Table VII to determine the required $x^{2}$ -values. Illustrate your work graphically.
For a $x^{2}$ -curve with 19 degrees of freedom, determine the $x^{2}-$ value that has area
a. 0.025 to its right.
b. 0.95 to its right.

Tyler Moulton
Tyler Moulton
Numerade Educator
01:02

Problem 6

Use Table VII to determine the required $x^{2}$ -values. Illustrate your work graphically.
For a $x^{2}$ -curve with 22 degrees of freedom, determine the $x^{2}$ -value that has area
a. 0.01 to its right.
b. 0.995 to its right.

Tyler Moulton
Tyler Moulton
Numerade Educator
01:03

Problem 7

Use Table VII to determine the required $x^{2}$ -values. Illustrate your work graphically.
For a $x^{2}$ -curve with df $=10,$ determine
a. $x_{0}^{2}$
b. $x_{0.975}^{2}$

Tyler Moulton
Tyler Moulton
Numerade Educator
01:02

Problem 8

Use Table VII to determine the required $x^{2}$ -values. Illustrate your work graphically.
For a $x^{2}$ -curve with df $=4,$ determine
a. $x_{0.005}^{2}$
b. $x_{0.99}^{2}$

Tyler Moulton
Tyler Moulton
Numerade Educator
01:03

Problem 9

Extending the Concepts and Skills
Explain how you would use Table VII to find the $x^{2}$ -value that has area 0.05 to its left. Obtain this $x^{2}$ -value for a $x^{2}$ -curve with df $=26.$

Tyler Moulton
Tyler Moulton
Numerade Educator
01:20

Problem 10

Explain how you would use Table VII to find the two $x^{2}$ -values that divide the area under a $x^{2}$ -curve into a middle 0.95 area and two outside 0.025 areas. Find these two $x^{2}$ -values for a $x^{2}$ -curve with $\mathrm{df}=14.$

Tyler Moulton
Tyler Moulton
Numerade Educator