Question 334128: The County Executive for Monroe County is concerned about the response time for the three fire companies in the county. Samples of the response times (in minutes) for each company follow. At the 0.05 significance level is there a difference in the mean response time?
Youngsville
2.2
1.2
1.9
3.1
1.8
1.5
Northeast
2.3
1.5
1.2
1.4
2.2
Corry
0.9
0.8
1.1
1.2
0.7
a. State the null and alternate hypotheses.
b. State the decision rule.
c. Compute the value of the test statistic (use the tables).
d. What is your decision regarding the null hypothesis? Interpret the result.
Answer by jrfrunner(365)   (Show Source):
You can put this solution on YOUR website! Let  =population mean response for the youngsville station
Let  =population mean response for the Northeast station
Let  =population mean response for the Corry station
--
Ho: ==
Ha: Not all the means are equal (ie some difference exist)
--
Carry out a one way ANOVA test and reject the null hypothesis if F test > Fcritical or reject if pvalue<
---
ANOVA requires Normality and homogeneity of variances, both things should be tested before conducting the ANOVA, I'll assume this is all ok to proceed
--
From ANOVA table, Ftest=5.77, Fcritical=3.81 (at  )
also pvalue=0.016
--
therefore, since Ftest=5.77>Fcritical=3.81 and since pvalue=0.016<, reject Ho
--
conclusion: Not all the means are equal
--
The next question, should be: if they are not all equal, where are the differences?
==========
NOTE:
At this point you would have to carry out pairwise comparisons (there are 3C2=3 comparisons to conduct in this problem to find where the diffences lie, BUT... you need to make sure not to inflate the "overall" type I () error.
This can be done in many ways, boneforri correction to the value is one method but other methods exist.
|
|
|
