252y0521s 3/25/05
First take-home problem – based on 9.26 on page E-48
————— 3/25/2005 1:54:04 AM ————————————————————
Welcome to Minitab, press F1 for help.
MTB > WOpen "C:\Documents and Settings\rbove\My Documents\Minitab\252x05021.MTW".
Retrieving worksheet from file: 'C:\Documents and Settings\rbove\My
Documents\Minitab\252x0502-1.MTW'
Worksheet was saved on Fri Mar 25 2005
Results for: 252x0502-1.MTW
MTB > print c1-c4
Data Display
Row
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
x1
45.14
10.11
29.38
19.65
16.25
29.46
8.13
45.63
24.49
12.71
37.04
x2
9.55
38.76
16.65
19.00
17.00
29.01
12.34
11.18
12.15
14.40
8.00
16.19
33.46
18.37
9.86
rx1
10
2
7
5
4
8
1
11
6
3
9
rx2
2
15
9
12
10
13
6
4
5
7
1
8
14
11
3
Descriptive Statistics: x1, x2
Variable
x1
x2
N
11
15
N*
0
0
Mean
25.27
17.73
SE Mean
4.02
2.35
StDev
13.33
9.11
Minimum
8.13
8.00
Q1
12.71
11.18
Median
24.49
16.19
Q3
37.04
19.00
Maximum
45.63
38.7
MTB > TwoSample c1 c2;
SUBC>
Pooled.
Two-Sample T-Test and CI: x1, x2
Two-sample T for x1 vs x2
x1
x2
N
11
15
Mean
25.3
17.73
StDev
13.3
9.11
SE Mean
4.0
2.4
Difference = mu (x1) - mu (x2)
Estimate for difference: 7.54382
95% CI for difference: (-1.52083, 16.60847)
T-Test of difference = 0 (vs not =): T-Value = 1.72
Both use Pooled StDev = 11.0641
P-Value = 0.099
DF = 24
MTB > TwoSample c1 c2.
Two-Sample T-Test and CI: x1, x2
Two-sample T for x1 vs x2
x1
x2
N
11
15
Mean
25.3
17.73
StDev
13.3
9.11
SE Mean
4.0
2.4
Difference = mu (x1) - mu (x2)
1
252y0521s 3/25/05
Estimate for difference: 7.54382
95% CI for difference: (-2.32775, 17.41539)
T-Test of difference = 0 (vs not =): T-Value = 1.62
P-Value = 0.125
DF = 16
MTB > VarTest c1 c2;
SUBC>
Unstacked.
Test for Equal Variances: x1, x2
95% Bonferroni confidence intervals for standard deviations
x1
x2
N
11
15
Lower
8.87606
6.39055
StDev
13.3313
9.1054
Upper
25.6219
15.4332
F-Test (normal distribution)
Test statistic = 2.14, p-value = 0.187
Levene's Test (any continuous distribution)
Test statistic = 2.96, p-value = 0.098
Test for Equal Variances for x1, x2
Test for Equal Variances for x1, x2
F-Test
Test Statistic
P-Value
x1
2.14
0.187
Lev ene's Test
Test Statistic
P-Value
x2
5
10
15
20
95% Bonferroni Confidence Intervals for StDevs
2.96
0.098
25
x1
x2
10
20
30
Data
40
50
MTB > Mann-Whitney 95.0 c1 c2;
SUBC>
Alternative 0.
Mann-Whitney Test and CI: x1, x2
x1
x2
N
11
15
Median
24.49
16.19
Point estimate for ETA1-ETA2 is 6.87
95.1 Percent CI for ETA1-ETA2 is (-2.12,17.31)
W = 178.0
Test of ETA1 = ETA2 vs ETA1 not = ETA2 is significant at 0.1323
2
252y0521s 3/25/05
MTB > NormTest c2;
SUBC>
KSTest.
Probability Plot of x2
Probability Plot of x2
Normal
99
Mean
StDev
N
KS
P-Value
95
90
17.73
9.105
15
0.244
0.024
Percent
80
70
60
50
40
30
20
10
5
1
0
10
20
30
40
x2
MTB > NormTest c1;
SUBC>
KSTest.
Probability Plot of x1
Probability Plot of x1
Normal
99
Mean
StDev
N
KS
P-Value
95
90
25.27
13.33
11
0.118
>0.150
Percent
80
70
60
50
40
30
20
10
5
1
0
10
20
30
40
50
60
x1
MTB >
3
252y0521s 3/25/05
First take-home problem – based on 9.26 on page E-48
Lilliefors computations.
————— 4/7/2005 10:01:12 PM ————————————————————
Welcome to Minitab, press F1 for help.
MTB > WOpen "C:\Documents and Settings\rbove\My Documents\Minitab\notmuch.MTW".
Retrieving worksheet from file: 'C:\Documents and Settings\rbove\My
Documents\Minitab\notmuch.MTW'
Worksheet was saved on Fri Jan 21 2005
Results for: 252x0502-1.MTW
MTB
MTB
MTB
MTB
MTB
>
>
>
>
>
let c10=c1
let c11 = c10*c10
let k10 = sum(c10)
let k11=sum(c11)
print k10, k11
Data Display
K10
K11
277.990
8802.55
MTB > let k10 = k10/11
MTB > print k10
Data Display
K10
25.2718
MTB > let k12 = 11*k10*k10
MTB > print k11 k12
Data Display
K11
K12
8802.55
7025.31
MTB > let k11=k12-k11
MTB > print k11
Data Display
K11
-1777.24
MTB > describe c10
Descriptive Statistics: x
Variable
x
N
11
N*
0
Mean
25.27
SE Mean
4.02
StDev
13.33
Minimum
8.13
Q1
12.71
Median
24.49
Q3
37.04
Maximum
45.63
MTB > let k11 = k11/10
MTB > print k11
Data Display
K11
177.724
MTB > let k11 = sqrt(k11)
MTB > print k11
Data Display
K11
13.3313
MTB > Center c10 c13.
MTB > describe c13
Descriptive Statistics: C13
4
252y0521s 3/25/05
Variable
C13
Variable
C13
N N*
Mean
11
0 -1.11022E-16
Maximum
1.527
SE Mean
0.302
StDev
1.000
Minimum
-1.286
Q1
-0.942
Median
-0.0586
Q1
12.71
Median
24.49
Q3
37.04
Minimum
-17.14
Q1
-12.56
Median
-0.782
Q3
0.883
MTB > describe c10
Descriptive Statistics: x
Variable
x
N
11
N*
0
Mean
25.27
SE Mean
4.02
StDev
13.33
Minimum
8.13
Maximum
45.63
MTB > print k10 k11
Data Display
K10
K11
25.2718
13.3313
MTB > let c12 = c10-k10
MTB > describe c12
Descriptive Statistics: C12
Variable
C12
Variable
C12
N N*
Mean
11
0 -1.11022E-15
Maximum
20.36
SE Mean
4.02
StDev
13.33
Q3
11.77
MTB > let c12 = c10-k10
MTB > print k11
Data Display
K11
13.3313
MTB >
MTB >
MTB >
MTB >
MTB >
MTB >
MTB >
MTB >
MTB >
SUBC>
MTB >
SUBC>
MTB >
SUBC>
MTB >
let c12 = c12/k11
let c12 = c12 * 10000
let c12 = c12/100
let c14 = c12
round c12 c14
let c12 = c14/100
let c15=c14
let c16 = c15/11
CDF c13 c17;
Normal 0.0 1.0.
Sort c10 c11 c12 c17 c10 c11 c12 c17;
By c10.
sort c13 c13;
by c1.
let c18 = c16 - c17
MTB > let c18 = abs(c18)
MTB > print c10 c11 c12 c14 c15 c16 c17 c18
Data Display
Row
1
2
3
4
5
6
7
8
9
10
11
x
8.13
10.11
12.71
16.25
19.65
24.49
29.38
29.46
37.04
45.14
45.63
xsq
66.10
102.21
161.54
264.06
386.12
599.76
863.18
867.89
1371.96
2037.62
2082.10
zrnd
-1.29
-1.14
-0.94
-0.68
-0.42
-0.06
0.31
0.31
0.88
1.49
1.53
Descriptive Statistics: D
Variable
D
Variable
D
N N*
Mean
11
0 0.0614
Maximum
0.1179
O
1
1
1
1
1
1
1
1
1
1
1
SE Mean
0.0131
CumO
1
2
3
4
5
6
7
8
9
10
11
StDev
0.0433
Fo
0.09091
0.18182
0.27273
0.36364
0.45455
0.54545
0.63636
0.72727
0.81818
0.90909
1.00000
Minimum
0.00687
Fe
0.099251
0.127705
0.173025
0.249286
0.336622
0.476617
0.621020
0.623301
0.811314
0.931932
0.936631
Q1
0.0153
D
0.008342
0.054114
0.099702
0.114351
0.117924
0.068837
0.015344
0.103972
0.006868
0.022842
0.063369
Median
0.0634
Q3
0.1040
5
252y0521s 3/25/05
Wilcoxon Paired Problem Lee p612
Row
x1
1
2
3
4
5
6
40
35
42
30
63
36
x 2 d  x 2  x1
62
49
39
28
66
40
Row
x1
1
40
2
35
3
42
4
30
5
55
6
63
7
36
Variable n
7
x1
x2
d
-22
-14
3
2
-3
-4
d
22
14
3
2
3
4
r
r*
6.0
5.0
2.5
1.0
2.5
4.0
6.05.02.5+
1.0+
2.54.0-
x 2 d  x 2  x1
62
49
39
28
55
66
40
-22
-14
3
2
0
-3
-4
Mean
43.00
SE Mean StDev
4.46 11.80
7
48.43
5.15
13.62
7
-5.43
3.49
9.24
Teaching Problem Bassett p134
MTB > TwoSample c1 c2;
SUBC>
Pooled;
SUBC>
Alternative -1.
Two-Sample T-Test and CI: x1, x2
Two-sample T for x1 vs x2
N
Mean StDev SE Mean
x1 250 68.45
7.96
0.50
x2 150 70.62
7.06
0.58
Difference = mu (x1) - mu (x2)
Estimate for difference: -2.17521
95% upper bound for difference: -0.87525
T-Test of difference = 0 (vs <): T-Value = -2.76
P-Value = 0.003
DF = 398
P-Value = 0.002
DF = 343
MTB > TwoSample c1 c2;
SUBC>
Alternative -1.
Two-Sample T-Test and CI: x1, x2
Two-sample T for x1 vs x2
x1
x2
N
250
150
Mean
68.45
70.62
StDev
7.96
7.06
SE Mean
0.50
0.58
Difference = mu (x1) - mu (x2)
Estimate for difference: -2.17521
95% upper bound for difference: -0.91322
T-Test of difference = 0 (vs <): T-Value = -2.84
MTB > VarTest c1 c2;
SUBC>
Unstacked.
Test for Equal Variances: x1, x2
F-Test (normal distribution)
Test statistic = 1.27, p-value = 0.107
6
252y0521s 3/25/05
Marble Problem
One-Sample T: x1
Test of mu = 12 vs < 12
Variable
x1
N
105
Mean
12.0150
StDev
0.0498
SE Mean
0.0049
95%
Upper
Bound
12.0231
T
3.09
P
0.999
ChiSquare Problem
————— 3/30/2005 10:22:03 PM ————————————————————
Welcome to Minitab, press F1 for help.
Results for: 252x0502-7.MTW
MTB > WSave "C:\Documents and Settings\rbove\My Documents\Minitab\252x05027.MTW";
SUBC>
Replace.
Saving file as: 'C:\Documents and Settings\rbove\My
Documents\Minitab\252x0502-7.MTW'
MTB > sum c1
Sum of O
Sum of O = 180
MTB > echo
MTB > Execute "C:\Documents and Settings\rbove\My
Documents\Minitab\252chisq.mtb" 1.
Executing from file: C:\Documents and Settings\rbove\My
Documents\Minitab\252chisq.mtb
MTB > #252chisq
MTB > Name c1 'O' #O on c1, E in C2
MTB > Name c2 'E'
MTB > let c3='E'-'O'
MTB > let c4=c3*c3
MTB > let c5=c4/'E'
MTB > let c6='O'*'O' #Shortcut method
MTB > let c6=c6/'E'
MTB > print c1-c6
Data Display
Row
1
2
3
4
5
MTB
MTB
MTB
MTB
MTB
MTB
MTB
MTB
O
42
33
35
25
45
>
>
>
>
>
>
>
>
E
36
36
36
36
36
C3
-6
3
1
11
-9
C4
36
9
1
121
81
C5
1.00000
0.25000
0.02778
3.36111
2.25000
C6
49.0000
30.2500
34.0278
17.3611
56.2500
name k1 'n'
let k1=sum(c1) #k1=k2=n
let k2=sum(c2)
let k3=sum(c3) #Should be zero
let k5=sum(c5)
name k5 'chisq'
let k6=sum(c6)
name k4 'chisq1'
7
252y0521s 3/25/05
MTB > let k4=k6-k1
MTB > print k1-k6
Data Display
n
K2
K3
chisq1
chisq
K6
180.000
180.000
0
6.88889
6.88889
186.889
MTB > end
MTB > Save "C:\Documents and Settings\rbove\My Documents\Minitab\252x05027.MTW";
SUBC>
Replace.
Saving file as: 'C:\Documents and Settings\rbove\My
Documents\Minitab\252x0502-7.MTW'
Existing file replaced.
MTB >
8