a.
Check whether there is any difference in the mean drainage times for the different channel designs or not.
a.
Answer to Problem 11SE
There is sufficient evidence to conclude that there is a significant difference in the mean drainage times with different channel type at
Explanation of Solution
Given info:
The design variable is the channel type and the response is the drainage time. The table provides the drainage time corresponding to the channel type.
Calculation:
State the hypotheses:
Null hypothesis:
Alternative hypothesis:
The ANOVA table can be obtained as follows:
Software procedure:
Step by step procedure to obtain One-Way ANOVA using the MINITAB software:
- Choose Stat > ANOVA > One-Way.
- In Response, enter the column of Drainage time.
- In Factor, enter the column of Channel type.
- In Confidence level, enter 0.95.
- Click OK.
Output using the MINITAB software is given below:
From the ANOVA table, it is clear that P-value is 0.001 and the F-value is 8.71.
Since, the level of significance is not specified; the prior level of significance
Decision:
If
If
Conclusion:
Here, the P-value is less than the level of significance.
That is,
By rejection rule, reject the null hypothesis.
There is sufficient evidence to conclude that there is a significant difference in the mean drainage times with different channel type at
b.
Identify the pairs of designs that can conclude to have differing mean drainage times.
b.
Answer to Problem 11SE
There is sufficient evidence to conclude that the channels 3 and 4 differ from channels 1,2, and 5 at
Explanation of Solution
Calculation:
State the hypotheses:
Null hypothesis:
Alternative hypothesis:
Decision:
By Tukey-Kramer method for multiple comparisons,
If
If
Here
From Appendix A table A.9, the upper 5% point of the
For comparing channel 1 and 2:
The 5% critical value is,
Substitute
The sample means are,
Now,
Which is less than 4.51.
Thus, fail to reject the null hypothesis
Hence, for channel 1 and 2 there is no difference in mean drainage times.
For comparing channel 1 and 3:
The 5% critical value is,
Substitute
The sample means are,
Now,
Which is greater than 4.51.
Thus, reject the null hypothesis
Hence, for channel 1 and 3 there is difference in mean drainage times.
For comparing channel 1 and 4:
The 5% critical value is,
Substitute
The sample means are,
Now,
Which is greater than 4.51.
Thus, reject the null hypothesis
Hence, for channel 1 and 4 there is difference in mean drainage times.
For comparing channel 1 and 5:
The 5% critical value is,
Substitute
The sample means are,
Now,
Which is less than 4.51.
Thus, fail to reject the null hypothesis
Hence, for channel 1 and 5 there is no difference in mean drainage times.
For comparing channel 2 and 3:
The 5% critical value is,
Substitute
Now,
Which is greater than 4.51.
Thus, reject the null hypothesis
Hence, for channel 2 and 3 there is difference in mean drainage times.
For comparing channel 2 and 4:
The 5% critical value is,
Substitute
Now,
Which is greater than 4.51.
Thus, reject the null hypothesis
Hence, for channel 2 and 4 there is difference in mean drainage times.
For comparing channel 2 and 5:
The 5% critical value is,
Substitute
Now,
Which is less than 4.51.
Thus, fail to reject the null hypothesis
Hence, for channel 2 and 5 there is no difference in mean drainage times.
For comparing channel 3 and 4:
The 5% critical value is,
Substitute
Now,
Which is less than 4.51.
Thus, fail to reject the null hypothesis
Hence, for channel 3 and 4 there is no difference in mean drainage times.
For comparing channel 3 and 5:
The 5% critical value is,
Substitute
Now,
Which is greater than 4.51.
Thus, reject the null hypothesis
Hence, for channel 3 and 5 there is difference in mean drainage times.
For comparing channel 4 and 5:
The 5% critical value is,
Substitute
Now,
Which is greater than 4.51.
Thus, reject the null hypothesis
Hence, for channel 4 and 5 there is difference in mean drainage times.
Conclusion:
There is sufficient evidence to conclude that the channels 3 and 4 differ from channels 1,2, and 5 at
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Chapter 9 Solutions
Statistics for Engineers and Scientists
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