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Graded Assignment 4
The data set GOLFBALL is in problem 11.14 of the text 9th or 10th edition or on the CD. You must answer
at least the following questions versions A, B and C of the problem.
Only neat and legible papers with written answers in complete sentences will be read!
a) At a 5% level is there evidence of a difference in the average distance traveled by the golf balls with
different designs? Why? c) What assumptions are necessary in (a)? e) What golf ball design should be
chosen?
Do this problem in Excel as follows.
Use columns A, B, C, E and F on the Excel spreadsheet for data
In the first row of Columns B, C, D and F put in Des 1, Des 2, Des 3 and Des 4. Label Column E with Des
4a and Column A with ‘golfer.’ Starting in Cell A2 Put in the letters A through J to identify the golfers –
unless, of course, you want to suggest some names.
Now put in the data in columns B, C, D and F, skipping column D
Version A
To fill column E in cell E2 write =F2 after your 'enter' this cell should read '213.9'
Use the fill handle on cell E2 to make column E identical to column F except for the heading. Do not go on
unless this is true. Save your data as gdataA.xls
Use the 'tools' pull-down menu and pick 'data analysis' (If you cannot find this, use Tools and Add-Ins to
put in the analysis packs.)
Pick 'ANOVA: Single Factor. Set input range to $B$1:$E$11. Select 'New worksheet ply' and 'columns' ,
check 'labels in first row' hit 'OK' and save your results as gresltA.xls.
Version B
In order to check for the effect of the fact that the data is blocked by employees, repeat the analysis using
‘ANOVA: Two-Factor without replication. Set input range to $A$1:$E$11, check ‘labels,’ and save your
results as gresltB.xls
Version C
Take the last digit of your student number (if it's zero, use 10) and add 5 to it. Call this x and make sure
that I know its value. Go back to your original data or use the 'file' pull-down menu to open gresltA.xls.
To fill column E this time in cell E2 write =F2+ x .Now highlight cell E2 and use the fill handle to make
column E equal to column F plus x . Do not go on unless this is true. Save your data as gdataC.xls.
Run the one-way ANOVA again and save your results as gresltC.xls
Submit the data and results with your Student number. The most effective way to do this is to paste the
results into a Word document and then add neat hand or typed notes. Indicate what hypotheses were tested,
what the p-value was and whether, using the p-value, you would reject the null if (i) the significance level
was 5% and (ii) the significance level was 10%, explaining why. You will have two answers for each of
your two problems.
For your version C ANOVA do a Scheffe confidence interval and a Tukey-Kramer interval or procedure for
each of the C 24  6 possible differences between means and report which are different at the 5% level
according to each of the 2 methods. Answer as much as you can of the questions in Problem 11.14. The
extra credit below may be needed for a really complete answer.
Extra Credit: Take the data from your last ANOVA and perform a Levene test on it using the third
example in 252mvarex. as a pattern for your calculations. Make sure that you explain what is being tested
and what you conclude. Hand in separately – this will be treated as extra credit on your next take-home
exam.
Extra Extra Credit: Do a Bartlett test using the example in 252mvar as your pattern. It turns out that your
ANOVA has just enough columns to do this test.
gdataA
Golfer
1
2
3
4
5
6
7
8
9
10
Des 1
206.32
223.85
207.94
224.79
206.19
229.75
204.45
228.51
209.65
221.44
Des 2
203.81
223.85
206.75
223.97
205.68
234.3
204.49
219.5
210.86
233
Des 3
217.08
230.55
221.43
227.95
218.04
213.84
224.13
224.87
211.82
229.49
Des 4a
213.9
231.1
221.28
221.53
229.43
235.45
213.54
228.35
214.51
225.09
Des 4
213.9
231.1
221.28
221.53
229.43
235.45
213.54
228.35
214.51
225.09
Sum
2162.89
2166.21
2219.2
2234.18
Average
216.289
216.621
221.92
223.418
Variance
104.6483
139.6653
43.08287
60.3002
df
MS
132.6364
86.92417
F
1.525886
Average
210.2775
227.3375
214.35
224.56
214.835
228.335
211.6525
225.3075
211.71
227.255
Variance
38.96229
16.26729
65.66647
7.024667
127.2787
99.43723
87.47603
17.81042
4.272733
25.50057
gresltA
Anova: Single Factor
SUMMARY
Groups
Des 1
Des 2
Des 3
Des 4a
Count
10
10
10
10
ANOVA
Source of
Variation
Between Groups
Within Groups
SS
397.9091
3129.27
Total
3527.179
3
36
P-value
0.224397
F crit
2.866266
39
gresltB
Anova: Two-Factor Without Replication
SUMMARY
Count
1
2
3
4
5
6
7
8
9
10
4
4
4
4
4
4
4
4
4
4
Sum
841.11
909.35
857.4
898.24
859.34
913.34
846.61
901.23
846.84
909.02
2
Des 1
Des 2
Des 3
Des 4a
10
10
10
10
ANOVA
Source of
Variation
Rows
Columns
Error
SS
2058.09
397.9091
1071.18
Total
3527.179
gdataC
Golfer
1
2
3
4
5
6
7
8
9
10
Des 1
206.32
223.85
207.94
224.79
206.19
229.75
204.45
228.51
209.65
221.44
Des 2
203.81
223.85
206.75
223.97
205.68
234.3
204.49
219.5
210.86
233
2162.89
2166.21
2219.2
2234.18
216.289
216.621
221.92
223.418
104.6483
139.6653
43.08287
60.3002
df
MS
228.6766
132.6364
39.67334
F
5.763988
3.343212
9
3
27
P-value
0.00018
0.033859
F crit
2.250131
2.960351
P-value
0.000573
F crit
2.866266
39
Des 3
217.08
230.55
221.43
227.95
218.04
213.84
224.13
224.87
211.82
229.49
Des 4c
223.9
241.1
231.28
231.53
239.43
245.45
223.54
238.35
224.51
235.09
Des 4
213.9
231.1
221.28
221.53
229.43
235.45
213.54
228.35
214.51
225.09
Sum
2162.89
2166.21
2219.2
2334.18
Average
216.289
216.621
221.92
233.418
Variance
104.6483
139.6653
43.08287
60.3002
df
MS
639.703
86.92417
F
7.359323
gresltC
Anova: Single Factor
SUMMARY
Groups
Des 1
Des 2
Des 3
Des 4c
Count
10
10
10
10
ANOVA
Source of
Variation
Between Groups
Within Groups
SS
1919.109
3129.27
Total
5048.379
3
36
39
3
————— 4/5/2005 11:23:01 PM ————————————————————
Welcome to Minitab, press F1 for help.
MTB > WOpen "C:\Documents and Settings\rbove\My Documents\Minitab\2gr4051C.MTW".
Retrieving worksheet from file: 'C:\Documents and Settings\rbove\My
Documents\Minitab\2gr4-051C.MTW'
Worksheet was saved on Tue Apr 05 2005
Results for: 2gr4-051C.MTW
MTB > describe c2-c5
Descriptive Statistics: Des 1, Des 2, Des 3, Des 4
Variable
Des 1
Des 2
Des 3
Des 4
N
10
10
10
10
N*
0
0
0
0
Variable
Des 1
Des 2
Des 3
Des 4
Maximum
229.75
234.30
230.55
240.45
Mean
216.29
216.62
221.92
228.42
SE Mean
3.23
3.74
2.08
2.46
StDev
10.23
11.82
6.56
7.77
Minimum
204.45
203.81
211.82
218.54
Q1
206.29
205.38
216.27
219.36
Median
215.55
215.18
222.78
228.31
Q3
225.72
226.23
228.34
234.85
MTB > AOVOneway c2-c5.
One-way ANOVA: Des 1, Des 2, Des 3, Des 4
Source
Factor
Error
Total
DF
3
36
39
S = 9.323
SS
971.0
3129.3
4100.3
MS
323.7
86.9
R-Sq = 23.68%
F
3.72
P
0.020
R-Sq(adj) = 17.32%
MTB > vartest c2-c5;
SUBC> unstacked.
Test for Equal Variances: Des 1, Des 2, Des 3, Des 4
95% Bonferroni confidence intervals for standard deviations
N
Lower
StDev
Upper
Des 1 10 6.40248 10.2298 22.6233
Des 2 10 7.39650 11.8180 26.1357
Des 3 10 4.10804
6.5638 14.5159
Des 4 10 4.86006
7.7653 17.1731
Bartlett's Test (normal distribution)
Test statistic = 3.51, p-value = 0.320
Levene's Test (any continuous distribution)
Test statistic = 3.78, p-value = 0.019
4
Test for Equal Variances: Des 1, Des 2, Des 3, Des 4
Test for Equal Variances for Des 1, Des 2, Des 3, Des 4
Bartlett's Test
Test Statistic
P-Value
Des 1
3.51
0.320
Lev ene's Test
Test Statistic
P-Value
Des 2
3.78
0.019
Des 3
Des 4
25
20
15
10
5
95% Bonferroni Confidence Intervals for StDevs
------------------------------------------------------------------------------
Bartlett Test Setup
MTB > stdev c2 k2
Standard Deviation of Des 1
Standard deviation of Des 1 = 10.2298
MTB > stdev c3 k3
Standard Deviation of Des 2
Standard deviation of Des 2 = 11.8180
MTB > stdev c4 k4
Standard Deviation of Des 3
Standard deviation of Des 3 = 6.56375
MTB > stdev c5 k5
Standard Deviation of Des 4
Standard deviation of Des 4 = 7.76532
MTB > print k2-k5
Data Display
K2
K3
K4
K5
MTB
MTB
MTB
MTB
MTB
MTB
10.2298
11.8180
6.56375
7.76532
>
>
>
>
>
>
stack k2-k5 c10
let c11 = c10*c10
let c12 = logten(c11)
let k11 = mean(c11)
let k12 = logten(k11)
print k11 k12
5
Data Display
K11
K12
86.9242
1.93914
MTB > print c10-c12
Data Display
Row
1
2
3
4
stdev
10.2298
11.8180
6.5638
7.7653
var
104.648
139.665
43.083
60.300
log
2.01973
2.14509
1.63430
1.78032
----------------------------------------------------------------------------------------------------------------
Levene Test
MTB
MTB
MTB
MTB
MTB
MTB
MTB
MTB
MTB
MTB
MTB
MTB
MTB
>
>
>
>
>
>
>
>
>
>
>
>
>
let c22 = c2
let c23 = c3
let c24 = c4
let c25 = c5
let k22 = median(c22)
let k23 = median(c23)
let k24 = median (c24)
let k25 = median(c25)
let c22 = c22 - k22
let c23 = c23 - k23
let c24 = c24 - k24
let c25 = c25 - k25
describe c22-c25
Descriptive Statistics: C22, C23, C24, C25
Variable
C22
C23
C24
C25
N
10
10
10
10
N*
0
0
0
0
Mean
0.744
1.44
-0.860
0.108
Variable
C22
C23
C24
C25
Maximum
14.20
19.12
7.77
12.14
SE Mean
3.23
3.74
2.08
2.46
StDev
10.23
11.82
6.56
7.77
C24
-5.70
7.77
-1.35
5.17
-4.74
-8.94
1.35
2.09
-10.96
6.71
C25
-9.41
7.79
-2.03
-1.78
6.12
12.14
-9.77
5.04
-8.80
1.78
Minimum
-11.10
-11.37
-10.96
-9.77
Q1
-9.26
-9.80
-6.51
-8.95
Median
-1.42109E-14
0.000000000
0.000000000
0.000000000
Q3
10.17
11.05
5.55
6.54
MTB > print c21-c25
Data Display
Row
1
2
3
4
5
6
7
8
9
10
MTB
MTB
MTB
MTB
C21
>
>
>
>
let
let
let
let
C22
-9.225
8.305
-7.605
9.245
-9.355
14.205
-11.095
12.965
-5.895
5.895
c22
c23
c24
c25
=
=
=
=
C23
-11.37
8.67
-8.43
8.79
-9.50
19.12
-10.69
4.32
-4.32
17.82
absolute(c22)
absolute(c23)
absolute(c24)
absolute(c25)
6
MTB > print c22 - c25
Data Display
Row
1
2
3
4
5
6
7
8
9
10
C22
9.225
8.305
7.605
9.245
9.355
14.205
11.095
12.965
5.895
5.895
C23
11.37
8.67
8.43
8.79
9.50
19.12
10.69
4.32
4.32
17.82
C24
5.70
7.77
1.35
5.17
4.74
8.94
1.35
2.09
10.96
6.71
C25
9.41
7.79
2.03
1.78
6.12
12.14
9.77
5.04
8.80
1.78
MTB > AOVO c22-c25
One-way ANOVA: C22, C23, C24, C25
Source
Factor
Error
Total
DF
3
36
39
S = 3.741
Level
C22
C23
C24
C25
N
10
10
10
10
SS
158.8
503.7
662.6
MS
52.9
14.0
R-Sq = 23.97%
Mean
9.379
10.303
5.478
6.466
StDev
2.743
4.902
3.250
3.723
F
3.78
P
0.019
R-Sq(adj) = 17.64%
Individual 95% CIs For Mean Based on
Pooled StDev
--------+---------+---------+---------+(---------*--------)
(--------*---------)
(---------*---------)
(---------*--------)
--------+---------+---------+---------+5.0
7.5
10.0
12.5
Pooled StDev = 3.741
MTB >
7