Chapter 5.8, Problem 1E

Find the following values.

1. a. ${\chi }_{12,.025}^2$
2. b. ${\chi }_{12,.975}^2$
3. c. ${\chi }_{5,.055}^2$
4. d. ${\chi }_{5,.995}^2$
5. e. ${\chi }_{22,.1}^2$
6. f. ${\chi }_{22,.9}^2$

To determine

Find the value of ${\chi }_{12,0.025}^2$.

Answer to Problem 1E

The value of ${\chi }_{12,0.025}^2$ is 23.34.

Explanation of Solution

Calculation:

Software Procedure:

Step-by-step procedure to obtain the critical value using the MINITAB software:

• Choose Graph > Probability Distribution Plot choose View Probability> OK.
• From Distribution, choose ‘chi square distribution.
• In Degrees of freedom, enter 12.
• Click the Shaded Area tab.
• Choose Probability Value and Right Tail for the region of the curve to shade.
• Enter the Probability value as 0.025.
• Click OK.

Output using the MINITAB software is given below:

From the output, the value of ${\chi }_{12,0.025}^2$ is 23.34.

To determine

Find the value of ${\chi }_{12,0.975}^2$.

Answer to Problem 1E

The value of ${\chi }_{12,0.975}^2$ is 4.404.

Explanation of Solution

Calculation:

Software Procedure:

Step-by-step procedure to obtain the critical value using the MINITAB software:

• Choose Graph > Probability Distribution Plot choose View Probability> OK.
• From Distribution, choose ‘chi square distribution.
• In Degrees of freedom, enter 12.
• Click the Shaded Area tab.
• Choose Probability Value and Right Tail for the region of the curve to shade.
• Enter the Probability value as 0.975.
• Click OK.

Output using the MINITAB software is given below:

From the output, the value of ${\chi }_{12,0.975}^2$ is 4.404.

To determine

Find the value of ${\chi }_{5,0.005}^2$.

Answer to Problem 1E

The value of ${\chi }_{5,0.005}^2$ is 16.75.

Explanation of Solution

Calculation:

Software Procedure:

Step-by-step procedure to obtain the critical value using the MINITAB software:

• Choose Graph > Probability Distribution Plot choose View Probability> OK.
• From Distribution, choose ‘chi square distribution.
• In Degrees of freedom, enter 5.
• Click the Shaded Area tab.
• Choose Probability Value and Right Tail for the region of the curve to shade.
• Enter the Probability value as 0.005.
• Click OK.

Output using the MINITAB software is given below:

From the output, the value of ${\chi }_{5,0.005}^2$ is 16.75.

To determine

Find the value of ${\chi }_{5,0.995}^2$.

Answer to Problem 1E

The value of ${\chi }_{5,0.995}^2$ is 0.4117.

Explanation of Solution

Calculation:

Software Procedure:

Step-by-step procedure to obtain the critical value using the MINITAB software:

• Choose Graph > Probability Distribution Plot choose View Probability> OK.
• From Distribution, choose ‘chi square distribution.
• In Degrees of freedom, enter 5.
• Click the Shaded Area tab.
• Choose Probability Value and Right Tail for the region of the curve to shade.
• Enter the Probability value as 0.995.
• Click OK.

Output using the MINITAB software is given below:

From the output, the value of ${\chi }_{5,0.995}^2$ is 0.4117.

To determine

Find the value of ${\chi }_{22,0.1}^2$.

Answer to Problem 1E

The value of ${\chi }_{22,0.1}^2$ is 30.81.

Explanation of Solution

Calculation:

Software Procedure:

Step-by-step procedure to obtain the critical value using the MINITAB software:

• Choose Graph > Probability Distribution Plot choose View Probability> OK.
• From Distribution, choose ‘chi square distribution.
• In Degrees of freedom, enter 22.
• Click the Shaded Area tab.
• Choose Probability Value and Right Tail for the region of the curve to shade.
• Enter the Probability value as 0.1.
• Click OK.

Output using the MINITAB software is given below:

From the output, the value of ${\chi }_{22,0.1}^2$ is 30.81.

To determine

Find the value of ${\chi }_{22,0.9}^2$.

Answer to Problem 1E

The value of ${\chi }_{22,0.9}^2$ is 14.04.

Explanation of Solution

Calculation:

Software Procedure:

Step-by-step procedure to obtain the critical value using the MINITAB software:

• Choose Graph > Probability Distribution Plot choose View Probability> OK.
• From Distribution, choose ‘chi square distribution.
• In Degrees of freedom, enter 22.
• Click the Shaded Area tab.
• Choose Probability Value and Right Tail for the region of the curve to shade.
• Enter the Probability value as 0.9.
• Click OK.

Output using the MINITAB software is given below:

From the output, the value of ${\chi }_{22,0.9}^2$ is 14.04.