
Concept explainers
Using Table G, find the values for χ2 left and χ2 right.
a. α = 0.05, n = 12
b. α = 0.10, n = 20
c. α = 0.05, n = 27
d. α = 0.01, n = 6
e. α = 0.10, n = 41
(a)

To find: The critical values
Answer to Problem 3E
The critical values
Explanation of Solution
Given info:
Calculation:
Degrees of freedom:
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 11.
- Click the Shaded Area tab.
- Choose Probability value and Both Tail for the region of the curve to shade.
- Enter the Probability value as 0.05.
- Click OK.
Output using the MINITAB software is given below:
Thus, the critical values
(b)

To find: The critical values
Answer to Problem 3E
The critical values
Explanation of Solution
Given info:
Calculation:
Degrees of freedom:
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 19.
- Click the Shaded Area tab.
- Choose Probability value and Both Tail for the region of the curve to shade.
- Enter the Probability value as 0.10.
- Click OK.
Output using the MINITAB software is given below:
Thus, the critical values
(c)

To find: The critical values
Answer to Problem 3E
The critical values
Explanation of Solution
Given info:
Calculation:
Degrees of freedom:
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 26.
- Click the Shaded Area tab.
- Choose Probability value and Both Tail for the region of the curve to shade.
- Enter the Probability value as 0.05.
- Click OK.
Output using the MINITAB software is given below:
Thus, the critical values
(d)

To find: The critical values
Answer to Problem 3E
The critical values
Explanation of Solution
Given info:
Calculation:
Degrees of freedom:
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 Both Tail for the region of the curve to shade.
- Enter the Probability value as 0.01.
- Click OK.
Output using the MINITAB software is given below:
Thus, the critical values
(e)

To find: The critical values
Answer to Problem 3E
The critical values
Explanation of Solution
Given info:
Calculation:
Degrees of freedom:
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 40.
- Click the Shaded Area tab.
- Choose Probability value and Both Tail for the region of the curve to shade.
- Enter the Probability value as 0.10.
- Click OK.
Output using the MINITAB software is given below:
Thus, the critical values
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Chapter 7 Solutions
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