Using Table G, find the critical value(s) for each. Indicate the noncritical region or regions, and state the null and alternative hypotheses. Use σ2 = 225.
a. α = 0.10, n = 14, two-tailed
b. α = 0.05, n = 27, right-tailed
c. α = 0.01, n = 9, left-tailed
d. α = 0.05, n = 17, right-tailed
a.
To find: The critical values for two tailed test.
Answer to Problem 1E
The critical values for two tailed test is 5.892 and 23.362, respectively.
Null hypothesis:
Alternative hypothesis:
Explanation of Solution
Given info:
The level of significance is
Answer:
Degrees of freedom:
The area to the right of larger value is,
From “Table G: The chi square distribution”, the critical values for the
Critical and non critical region:
Software Procedure:
Step-by-step procedure to obtain the critical region and non critical using the MINITAB software:
- Choose Graph > Probability Distribution Plot > choose View Probability> OK.
- From Distribution, choose Chi-square.
- In Degrees of freedom, enter 13.
- 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:
State the null and alternative hypotheses:
Here, the claim is that the population variance is 225. This can be written as
Null hypothesis:
Alternative hypothesis:
b.
To find: The critical value for right tailed test.
Answer to Problem 1E
The critical value for right tailed test is 38.885.
Null hypothesis:
Alternative hypothesis:
Explanation of Solution
Given info:
The level of significance is
Answer:
Degrees of freedom:
From “Table G: The chi square distribution”, the critical values for the
Critical and non critical region:
Software Procedure:
Step-by-step procedure to obtain the critical region and non critical using the MINITAB software:
- Choose Graph > Probability Distribution Plot > choose View Probability> OK.
- From Distribution, choose Chi-square.
- In Degrees of freedom, enter 26.
- Click the Shaded Area tab.
- Choose Probability value and Right Tail for the region of the curve to shade.
- Enter the Probability value as 0.05.
- 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 value for left tailed test.
Answer to Problem 1E
The critical value for left tailed test is 1.646.
Null hypothesis:
Alternative hypothesis:
Explanation of Solution
Given info:
The level of significance is
Answer:
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
Critical and non critical region:
Software Procedure:
Step-by-step procedure to obtain the critical region and non critical using the MINITAB software:
- Choose Graph > Probability Distribution Plot > choose View Probability> OK.
- From Distribution, choose Chi-square.
- In Degrees of freedom, enter 8.
- Click the Shaded Area tab.
- Choose Probability value and Left Tail for the region of the curve to shade.
- Enter the Probability value as 0.01.
- 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 right tailed test.
Answer to Problem 1E
The critical value for right tailed test is 26.296.
Null hypothesis:
Alternative hypothesis:
Explanation of Solution
Given info:
The level of significance is
Answer:
Degrees of freedom:
From “Table G: The chi square distribution”, the critical values for the
Critical and non critical region:
Software Procedure:
Step-by-step procedure to obtain the critical region and non critical 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 0.05.
- 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
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