Question 285901: A corporate CEO reviews the earnings of three divisions over the last eighteen months. Each division reports its earnings quarterly. Based on the earnings below, is there sufficient evidence to conclude, at the 99% level of confidence, that one of these divisions is more profitable than the others?
Division I Division II Division III
42 40 7
39 32 1
32 27 11
1 11 15
49 25 16
54 23 8
· State the null and alternate hypotheses
· Calculate the sums of squares SS(total), SS(factor), and SS(error)
· Calculate the degrees of freedom df(total), df(factor), and df(error)
· Calculate the mean square for factor, and the mean square for error
· Calculate the F-statistic
· Determine the critical value(s)
· State your decision: Should the null hypothesis be rejected?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A corporate CEO reviews the earnings of three divisions over the last eighteen months. Each division reports its earnings quarterly. Based on the earnings below, is there sufficient evidence to conclude, at the 99% level of confidence, that one of these divisions is more profitable than the others?
Division I Division II Division III
42 40 7
39 32 1
32 27 11
1 11 15
49 25 16
54 23 8
· State the null and alternate hypotheses
Ho: the means are equal
Ha: at least one of the means is different
-------------------------
I ran ANOVA on the three data sets and got the following:
test stat: F = 6.72531057..
p-value: 0.00082..
Factor:
df=2
SS: 2153.44
MS: 1076.72
---
Error:
df=15
SS: 2401.5
MS: 160.1
Sxp=12.6531...
· Calculate the sums of squares SS(total), SS(factor), and SS(error)
· Calculate the degrees of freedom df(total), df(factor), and df(error)
· Calculate the mean square for factor, and the mean square for error
· Calculate the F-statistic
· Determine the critical value(s)
· State your decision: Should the null hypothesis be rejected?
Since the p-value is less than 1% reject Ho at the 99% significanc
level.
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Cheers,
Stan H.
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