Chapter 8.3, Problem 3E

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

To determine

To find: The critical value for t test when $n=12$, $\alpha =0.01$ and left tailed.

Answer to Problem 3E

The critical value is –2.718.

Explanation of Solution

Given info:

The sample size is, $n=12$, $\alpha =0.01$ and left tailed.

Calculation:

Degrees of freedom:

$\begin{array}{c}n=12-1\\ =11\end{array}$

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.

To determine

To find: The critical value for t test when $n=16$, $\alpha =0.05$ and right tailed.

Answer to Problem 3E

The critical value is +1.753.

Explanation of Solution

Given info:

The sample size is, $n=16$, $\alpha =0.05$ and right tailed.

Calculation:

Degrees of freedom:

$\begin{array}{c}n=16-1\\ =15\end{array}$

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.

To determine

To find: The critical value for t test when $n=17$, $\alpha =0.10$ and two tailed.

Answer to Problem 3E

The critical value is ±1.943.

Explanation of Solution

Given info:

The sample size is, $n=17$, $\alpha =0.10$ and two tailed.

Calculation:

Degrees of freedom:

$\begin{array}{c}n=17-1\\ =16\end{array}$

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.

To determine

To find: The critical value for t test when $n=11$, $\alpha =0.025$ and right tailed.

Answer to Problem 3E

The critical value is +2.228.

Explanation of Solution

Given info:

The sample size is, $n=11$, $\alpha =0.025$ and right tailed.

Calculation:

Degrees of freedom:

$\begin{array}{c}n=11-1\\ =10\end{array}$

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.

To determine

To find: The critical value for t test when $n=10$, $\alpha =0.05$ and two tailed.

Answer to Problem 3E

The critical value is ±2.262.

Explanation of Solution

Given info:

The sample size is, $n=10$, $\alpha =0.05$ and two tailed.

Calculation:

Degrees of freedom:

$\begin{array}{c}n=10-1\\ =9\end{array}$

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.