a.
Construct an ANOVA table and give a
a.
Answer to Problem 17E
The ANOVA table is,
Source | DF | SS | MS | F | P |
Machine | 4 | 6,862 | 1,715.5 | 7.8823 | P-value<0.001 |
Error | 30 | 6,529.1 | 217.64 | ||
Total | 34 | 13,391 |
The range of P-value is
Explanation of Solution
Given info:
The design variable is the machine and the response is the processing time. The table provides the summary statistics of processing time corresponding to machine.
Calculation:
The ANOVA table can be obtained as follows:
There are four machines, therefore
The total number of observations is,
The degrees of freedom corresponding to the machine can be obtained as follows:
The degrees of freedom corresponding to the total can be obtained as follows:
The degrees of freedom corresponding to the error can be obtained as follows:
Total mean can be obtained as follows:
Substitute
The treatment sum of squares (SSTr) can be obtained as follows:
Substitut e
The error sum of squares (SSE) can be obtained as follows:
Substitute
The total sum of squares (SST) can be obtained as follows:
Substitute
The treatment mean square can be obtained as follows:
Substitute
The error mean square can be obtained as follows:
Substitute
The F-value can be obtained as follows:
Substitute
Thus, the F-value is 7.8823.
From Appendix A table A.8, the upper 0.1% point of the
Therefore, the range of P-value is
Thus, the ANOVA table is,
Source | DF | SS | MS | F | P |
Machine | 4 | 6,862 | 1,715.5 | 7.8823 | P-value<0.001 |
Error | 30 | 6,529.1 | 217.64 | ||
Total | 34 | 13,391 |
b.
Check whether the mean processing time differs for different machines.
b.
Answer to Problem 17E
There is sufficient evidence to conclude that the mean processing time differs for different machines.
Explanation of Solution
Calculation:
State the hypotheses:
Null hypothesis:
Alternative hypothesis:
From part (a), the F-ratio is 7.8823.
P-value:
From part (a), the P-value is less than 0.001.
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 the mean processing time differs for different machines at
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Chapter 9 Solutions
Statistics for Engineers and Scientists
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