Find the critical value (or values) for the t test for each.
a. n = 12, α = 0.01, left-tailed
b. n = 16, α = 0.05, right-tailed
c. n = 7, α = 0.10, two-tailed
d. n = 11, α = 0.025, right-tailed
e. n = 10, α = 0.05, two-tailed
a.
To find: The critical value for t test when
Answer to Problem 3E
The critical value is –2.718.
Explanation of Solution
Given info:
The sample size is,
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 ‘t’ distribution.
- In Degrees of freedom, enter 11.
- 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:
From the output, the critical value is –2.718.
b.
To find: The critical value for t test when
Answer to Problem 3E
The critical value is +1.753.
Explanation of Solution
Given info:
The sample size is,
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 ‘t’ distribution.
- In Degrees of freedom, enter 15.
- 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:
From the output, the critical value is +1.753.
c.
To find: The critical value for t test when
Answer to Problem 3E
The critical value is ±1.943.
Explanation of Solution
Given info:
The sample size is,
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 ‘t’ distribution.
- In Degrees of freedom, enter 16.
- Click the Shaded Area tab.
- Choose Probability Value and Two 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:
From the output, the critical value is ±1.943.
d.
To find: The critical value for t test when
Answer to Problem 3E
The critical value is +2.228.
Explanation of Solution
Given info:
The sample size is,
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 ‘t’ distribution.
- In Degrees of freedom, enter 10.
- 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 critical value is +2.228.
e.
To find: The critical value for t test when
Answer to Problem 3E
The critical value is ±2.262.
Explanation of Solution
Given info:
The sample size is,
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 ‘t’ distribution.
- In Degrees of freedom, enter 9.
- Click the Shaded Area tab.
- Choose Probability Value and Two 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:
From the output, the critical value is ±2.262.
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Chapter 8 Solutions
Elementary Statistics: A Step By Step Approach
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