SOLUTION: 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 suffici
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Question 251242: 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
45
33
22
50
18
59
Division II
13
27
12
17
14
7
Division III
4
18
24
19
18
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
45
33
22
50
18
59
Division II
13
27
12
17
14
7
Division III
4
18
24
19
18
8
•State the null and alternate hypotheses
Ho: The means are equal
H1: At least one of the means is different.
----------------------------------------------------------
I ran an ANOVA function on a TI-84 to get the following results:
SS= 2070.3333
MS= 1035.1667
Error SS= 1825.6667
Error MS= 121.7111
--------------------
•Calculate the sums of squares
.SS(total)=
.SS(factor)
.SS(error)
•Calculate the degrees of freedom
df(total),
df(factor)= 2
and df(error)= 15
•Calculate the mean square for factor, and the mean square for error
•Calculate the F-statistic = 8.5051
•Determine the critical value(s)
•State your decision: Should the null hypothesis be rejected?
p-value: 0.0034
Since the p-value is less than 5% reject Ho.
=================================================
Cheers,
Stan H.
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