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StatTools Assignment #4
– This assignment has two parts
Part I.
Requirements
1. ACCESS DATA.
You do not need to attach your Excel spreadsheet containing your simulated
data.
Since these are random samples, no two papers should contain the same results.
2. CHOOSE PROCEDURE and CALCULATE.
ANOVA Summary
Total Sample Size
144
Grand Mean
49.509
Pooled Std Dev
5.339
Pooled Variance
28.508
Number of Samples
4
Confidence Level
95.00%
Treatment 1
Treatment 2
Treatment 3
Treatment 4
ANOVA Sample Stats
Data Set #1
Data Set #1
Data Set #1
Data Set #1
Sample Size
36
36
36
36
Sample Mean
50.587
37.722
60.407
49.318
Sample Std Dev
5.254
4.417
6.398
5.097
Sample Variance
27.602
19.511
40.938
25.980
Pooling Weight
0.2500
0.2500
0.2500
0.2500
Sum of
Degrees of
Mean
FRatio
pValue
OneWay ANOVA Table
Squares
Freedom
Squares
Between Variation
9319.780
3
3106.593
108.973
< 0.0001
Within Variation
3991.102
140
28.508
Total Variation
13310.882
143
Difference
Tukey
Confidence Interval Tests
of Means
Lower
Upper
Treatment 1Treatment 2
12.865
9.631910256
16.09814937
Treatment 1Treatment 3
9.819
13.05236986
6.586130755
Treatment 1Treatment 4
1.269
1.963905198
4.502333912
Treatment 2Treatment 3
22.684
25.91739967
19.45116057
Treatment 2Treatment 4
11.596
14.82893501
8.362695899
Treatment 3Treatment 4
11.088
7.855345112
14.32158422
3. INTERPRET and COMMUNICATE CONCLUSIONS FOR THE FIRST
SIMULATION.
Respond to the following questions using complete sentences (exception made for the fillinthe
blank questions).
a.
Are the results of the oneway ANOVA Ftest what you expected?
Explain why or
why not using specific statistical information.
Of course, to answer this question you
must understand what is expected.
Answering the following questions should help you understand what is expected:
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View Full Documenti.
Do all of the populations have the same mean?
µ
1
=
50.59
µ
2
=
37.72
_
µ
3
=
60.41
µ
4
=
49.32
_
ii.
What are the null and alternative hypotheses? (Be sure to use proper notation)
H
0
:
µ
1 =
µ
2 =
µ
3 =
µ
4
H
a
: not all
µ
i
are equal to each other
iii. Should you reject H
0
, or not? Are the ANOVA results what you expected?
Explain and support your answer with specific statistical information.
We should reject the H
0
because the pvalue of .0001 is smaller than
alpha of .05. Since the means of the populations used to obtain the four
samples are different, it makes sense that the
µ
i
are not equal. The
ANOVA results are what I expected because the grand mean is 49.51
and the mean of the population means is 50. Also, the standard deviation
for each population was 5 and the pooled standard deviation is 5.34.
b.
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