Using Table G, find the critical value(s) for each. Show the critical and noncritical regions, and state the appropriate null and alternative hypotheses. Use σ2 = 225.
a. α = 0.01, n = 17, right-tailed
b. α = 0.025, n = 20, left-tailed
c. α = 0.01, n = 13, two-tailed
d. α = 0.025, n = 29, left-tailed
a.
To find: The critical value for right tailed test.
Answer to Problem 2E
The critical value for right tailed test is 32.000.
Null hypothesis:
Alternative hypothesis:
Explanation of Solution
The level of significance is
Answer:
Degrees of freedom:
From “Table G: The chi square distribution”, the critical values for the
Software Procedure:
Degrees of freedom:
From “Table G: The chi square distribution”, the critical values for the
Software Procedure:
Step-by-step procedure to obtain the critical region using the MINITAB software:
- Choose Graph > Probability Distribution Plot > choose View Probability> OK.
- From Distribution, choose Chi-square.
- In Degrees of freedom, enter 16.
- Click the Shaded Area tab.
- Choose Probability value and Right Tail for the region of the curve to shade.
- Enter the Probability value as 0.01.
- Click OK.
Output using the MINITAB software is given below:
State the null and alternative hypotheses:
Null hypothesis:
Alternative hypothesis:
b.
To find: The critical value for left tailed test.
Answer to Problem 2E
The critical value for left tailed test is 8.907.
Null hypothesis:
Alternative hypothesis:
Explanation of Solution
The level of significance is
Solution:
Degrees of freedom:
If the test is left tail, the level of significance is subtracted from 1. That is,
From “Table G: The chi square distribution”, the critical values for the
Software Procedure:
Step-by-step procedure to obtain the critical region using the MINITAB software:
- Choose Graph > Probability Distribution Plot > choose View Probability> OK.
- From Distribution, choose Chi-square.
- In Degrees of freedom, enter 19.
- Click the Shaded Area tab.
- Choose Probability value and Left 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:
State the null and alternative hypotheses:
Null hypothesis:
Alternative hypothesis:
c.
To find: The critical values for two tailed test.
Answer to Problem 2E
The critical values for two tailed test is 3.074 and 28.299, respectively.
Null hypothesis:
Alternative hypothesis:
Explanation of Solution
Given info:
The level of significance is
Solution:
Degrees of freedom:
The area to the right of larger value is,
From “Table G: The chi square distribution”, the critical values for the
Software Procedure:
Step-by-step procedure to obtain the critical region using the MINITAB software:
- Choose Graph > Probability Distribution Plot > choose View Probability> OK.
- From Distribution, choose Chi-square.
- In Degrees of freedom, enter 12.
- 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:
State the null and alternative hypotheses:
Null hypothesis:
Alternative hypothesis:
d.
To find: The critical value for left tailed test.
Answer to Problem 2E
The critical value for left tailed test is 15.308.
Null hypothesis:
Alternative hypothesis:
Explanation of Solution
Given info:
The level of significance is
Solution:
Degrees of freedom:
If the test is left tail, the level of significance is subtracted from 1. That is,
From “Table G: The chi square distribution”, the critical values for the
Software Procedure:
Step-by-step procedure to obtain the critical region using the MINITAB software:
- Choose Graph > Probability Distribution Plot > choose View Probability> OK.
- From Distribution, choose Chi-square.
- In Degrees of freedom, enter 28.
- Click the Shaded Area tab.
- Choose Probability value and Left 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:
State the null and alternative hypotheses:
Null hypothesis:
Alternative hypothesis:
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Chapter 8 Solutions
Elementary Statistics: A Step By Step Approach
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- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage