An experiment was carried out to compare flow rates for four different types of nozzle.
a. Sample sizes were 5, 6, 7, and 6, respectively, and calculations gave f = 3.68. State and test the relevant hypotheses using α = .01
b. Analysis of the data using a statistical computer package yielded P-value = .029. At level .01, what would you conclude, and why?
a.
State and test the hypotheses at
Answer to Problem 35SE
The test hypotheses are:
Null hypothesis:
Alternative hypothesis:
The test reveals that the flow rates for the 4 types of nozzle are not significantly different.
Explanation of Solution
Given info:
An experiment conducted to compare the flow rates for 4 types of nozzle considered respective sample sizes 5, 6, 7, 6 with F statistic value
Calculation:
Let the average flow rates for the 4 types of nozzle be
The test hypotheses are:
Null hypothesis:
That is, the flow rates for 4 types of nozzle are equal.
Alternative hypothesis:
That is, the flow rates for at least 2 types of nozzle are not equal.
The test statistic value is found to be
Degrees of freedom (df):
The number of treatments is
The total number of observations is:
Thus, the total df is:
The error df for the one factor ANOVA or the denominator df is:
Thus, the degrees of freedom are 3, 20.
Level of significance:
The given level of significance is
Bounds of the P-value:
The Table A.9, the table for “Critical Values for F Distributions” shows that the F statistic value
Thus, the lower bound of the P-value is 0.01 and the upper bound of the P-value is 0.05.
Rejection rule:
If the
Conclusion:
Here, the P-value is greater than the level of significance.
That is,
Thus, the decision is “fail to reject the null hypothesis”.
Therefore, the data do not provide sufficient evidence to conclude that the flow rates vary for at least 2 types of nozzle.
That is, the flow rates for the 4 types of nozzle are not significantly different.
b.
Give the conclusion at level 0.01, if analysis of the yielded
Answer to Problem 35SE
It can be concluded that the flow rates for the 4 types of nozzle are not significantly different.
Explanation of Solution
Calculation:
Level of significance:
The given level of significance is
P-value:
From statistical computer package, the P-value is 0.029.
Rejection rule:
If the
Conclusion:
Here, the p-value greater than the level of significance.
That is,
Thus, the decision is “fail to reject the null hypothesis”.
Therefore, the data do not provide sufficient evidence to conclude that the flow rates vary for at least 2 types of nozzle.
That is, the flow rates for the 4 types of nozzle are not significantly different.
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Chapter 10 Solutions
EBK PROBABILITY AND STATISTICS FOR ENGI
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