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Introduction to Variance in Decision making

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Analysis of Variance Example
A manager wishes to determine whether the mean times required
to complete a certain task differ for the three levels of
employee training. He randomly selected 10 employees with each
of the three levels of training (Beginner, Intermediate and
Advanced). Do the data provide sufficient evidence to indicate
that the mean times required to complete a certain task differ
for at least two of the three levels of training? The data
is summarized in the table.
Level of Training
n
s
2
Advanced
10
24.2
21.54
Intermediate
10
27.1
18.64
Beginner
10
30.2
17.76
H
a
: The mean times required to complete a certain task differ
for at least two of the three levels of
training.
H
o
: The mean times required to complete a certain task do not
differ the three levels of training. ( µ
B
= µ
I
= µ
A
)
Assumptions: The samples were drawn independently and
randomly from the three populations. The time required to
complete the task is normally distributed for each of the three
levels of training. The populations have equal variances.
Test
Statistic:

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RR: or
Calculations: = 10(24.2 - 27.16...)
2
+
10(27.1 - 27.16...)
2
+ 10(30.2 - 27.16...)
2
= 180.066....
= 9(21.54) + 9(18.64) + 9(17.76) = 521.46
Source
df
MS
F
Treatments
2
90.033
4.662
Error
27
19.313
Total
29
Decision: Reject H
o
.
Conclusion: There is sufficient evidence to indicate that
the mean times required to complete a certain task differ for
at least two of the three levels of training.
Which pairs of means differ?

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Analysis of Variance Example A manager wishes to determine whether the mean times required to complete a certain task differ for the three levels of employee training. He randomly selected 10 employees with each of the three levels of training (Beginner, Intermediate and Advanced). Do the data provide sufficient evidence to indicate that the mean times required to complete a certain task differ for at least two of the three levels of training? The data is summarized in the table.     Level of Training n   s2 Advanced 10 24.2 21.54 Intermediate 10 27.1 18.64 Beginner 10 30.2 17.76 Ha: The mean times required to complete a certain task differ for at least two of the three levels of training.  Ho: The mean times required to complete a certain task do not differ the three levels of training. ( µB = µI = µA) Assumptions:   The samples were drawn independently and randomly from the three populations. The time required to complete the task is normally distributed for each of the three levels of training. The populations have equal variances. Test Statistic:  RR: or  Calculations:  =  10(24.2 - 27.16...)2 + 10(27.1 - 27.16...)2 + 10(30.2 - 27.16...)2 = 180.066.... ...
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