Probability and Statistics for Engineering and Science, 9th Edition

Probability and Statistics for Engineering and Science, 9th Edition

Authors: Jay L. Devore

ISBN-13: 978-1305251809

See our solution for Question 3E from Chapter 8 from Devore's Probability and Statistics for Engineering and Science.

Problem 3E

Chapter:
Problem:
For which of the given P-values would the null hypothesis...

Step-by-Step Solution

Step 1:

Given that, the level of significance of test is 0.05 i.e. $\alpha = 0.05$. Based on given P-values, the decision is made on the null hypothesis. That is reject or not.


 
Step 2

Decision criteria for p-value:

If ${\rm{P - value}} \le \alpha $, reject the null hypothesis.

If ${\rm{P - value > }}\alpha $, fail to reject the null hypothesis.

a.

The P-value is 0.001 and the level of significance is 0.05.

Conclusion:

Here, P-value $ = 0.001 < 0.05$.

That is, P-value is less than the level of significance.

Based on rejection rule, reject the null hypothesis.

For P-value=0.001, the null hypothesis is rejected.

Therefore, the given P-value the null hypothesis will be rejected.


 
Step 3:

b.

The P-value is 0.021 and the level of significance is 0.05.

Conclusion:

Here, P-value $ = 0.021 < 0.05$.

That is, P-value is less than the level of significance.

Based on rejection rule, reject the null hypothesis.

For P-value=0.021, the null hypothesis is rejected.

Therefore, the given P-value the null hypothesis will be rejected.


 
Step 4:

c.

The P-value is 0.078 and the level of significance is 0.05.

Conclusion:

Here, P-value $ = 0.078 > 0.05$.

That is, P-value is greater than the level of significance.

Based on rejection rule, fail to reject the null hypothesis.

For P-value=0.078, the null hypothesis is failed to reject.

Therefore, the given P-value fail to reject the null hypothesis.


 
Step 5:

d.

The P-value is 0.047 and the level of significance is 0.05.

Conclusion:

Here, P-value $ = 0.047 < 0.05$.

That is, P-value is less than the level of significance.

Based on rejection rule, reject the null hypothesis.

For P-value=0.047, the null hypothesis is rejected.

Therefore, the given P-value the null hypothesis will be rejected.


 
Step 6:

e.

The P-value is 0.148 and the level of significance is 0.05.

Conclusion:

Here, P-value $ = 0.148 > 0.05$.

That is, P-value is greater than the level of significance.

Based on rejection rule, fail to reject the null hypothesis.

For P-value=0.148, the null hypothesis is failed to reject.

Therefore, the given P-value fail to reject the null hypothesis.