Question

Using Table F, find the P-value interval for each test value.
a. t = 3.025, n = 24, right-tailed
b. t = - 1.145, n = 5, left-tailed
c. t = 2.179, n = 13, two-tailed
d. t =  0.665, n = 10, right-tailed

Answer 1

a.

Find the P-value of t-statistic when t = 3.025, n = 24, and right-tailed.

From the “Appendix Table-F, t-distribution”, the t-value 3.025 is located with the corresponding level is less than 0.005.

Hence, the P-value interval is P-value < 0.005.

Use MINITAB to obtain the P-value.

 

MINITAB procedure:

Step 1: Choose Graph > Probability Distribution Plot choose View Probability > OK.

Step 2: From Distribution, choose ‘t’ distribution.

Step 3: In Degrees of freedom, enter 23.

Step 4: Click the Shaded Area tab.

Step 5: Choose X Value and Right Tail for the region of the curve to shade.

Step 6: Enter the data value as 3.025.

Step 7: Click OK.

 

MINITAB output:

 

From the above MINITAB output, the P-value for right-tailed test is 0.003.

 

b.

Find the P-value of t-statistic when t = -1.145, n = 5, and left-tailed.

From the “Appendix Table-F, t-distribution”, the t-value –1.145 is located between the corresponding level is 0.25 and 0.10.

Hence, the P-value interval is 0.10 < P-value < 0.25.

Use MINITAB to obtain the P-value.

 

MINITAB procedure:

Step 1: Choose Graph > Probability Distribution Plot choose View Probability > OK.

Step 2: From Distribution, choose ‘t’ distribution.

Step 3: In Degrees of freedom, enter 4.

Step 4: Click the Shaded Area tab.

Step 5: Choose X Value and Left Tail for the region of the curve to shade.

Step 6: Enter the data value as –1.145.

Step 7: Click OK.

 

MINITAB output:

 

From the above MINITAB output, the P-value for left-tailed test is 0.158.

c.

Find the P-value of t-statistic when t = 2.179, n = 13, and two-tailed.

From the “Appendix Table-F, t-distribution”, the t-value 2.179 is located with the corresponding level 0.05. Hence, the P-value interval is P-value = 0.05.

Use MINITAB to obtain the P-value.

 

MINITAB procedure:

Step 1: Choose Graph > Probability Distribution Plot choose View Probability > OK.

Step 2: From Distribution, choose ‘t’ distribution.

Step 3: In Degrees of freedom, enter 12.

Step 4: Click the Shaded Area tab.

Step 5: Choose X Value and Two Tail for the region of the curve to shade.

Step 6: Enter the data value as 2.179.

Step 7: Click OK.

 

MINITAB output:

 

From the above MINITAB output, the P-value for two-tailed test is, 2 × 0.02499 = 0.05.

 

d.

Find the P-value of t-statistic when t = 0.665, n = 10, and right-tailed.

From the “Appendix Table-F, t-distribution”, the t-value 0.665 is located with the corresponding level is greater than 0.25. Hence, the P-value interval is P-value > 0.25.

Use MINITAB to obtain the P-value.

 

MINITAB procedure:

Step 1: Choose Graph > Probability Distribution Plot choose View Probability > OK.

Step 2: From Distribution, choose ‘t’ distribution.

Step 3: In Degrees of freedom, enter 9.

Step 4: Click the Shaded Area tab.

Step 5: Choose X Value and right Tail for the region of the curve to shade.

Step 6: Enter the data value as 0.665.

Step 7: Click OK.

 

MINITAB output:

 

From the above MINITAB output, the P-value for right-tailed test is 0.261.

From the above MINITAB output, the P-value for right-tailed test is 0.261.