252y0621s1 11/4/06
Warning – This document has the worksheets for every version of Take-home
Problems 1 and 3. At last count it was about 50 pages long. Please only print the
solution for your version of the problem. Most versions are headed with problem
and version number.
The material on pages 1-5 is copies of the service method columns and is
largely copied into the take-home.
Individual solutions Take-home Problem 1 for Service Methods 2
through 11 start on page 6 and go to page 26. The order in which parts are
answered is
e) Test to see if the data from your method is Normally distributed (3)
f) Test to see if the standard deviations of the two methods are equal (1)
c) Test for a significant difference between the methods. Assume that the data represents a
Normally distributed population but the variances are not equal.
b) Test for a significant difference between the methods on the assumption that your method
represents data taken from the Normal distribution and the times have approximately equal variances. Use a
test ratio, critical value or a confidence interval (3) or all three (6).
d) Assume that the Normal distribution does not apply. (4)
The next few pages are a computer simulation of a pencil and paper
computation of the variances for Service Methods 6 and 9 and Lilliefors
computations for Service Method 4.
Individual solutions for Take-home Problem 3, versions 0 through 9 begin
about page 30. They are usually about 2 pages long.
a) Is there an association between the vehicle driven and behavior? I think that this calls for a chisquared test but comparison of two proportions was accepted for lesser credit.
b) Cut down the number of rows in the problem by adding together the people who stopped and
rolled through. Assume that you were testing the hypothesis that the proportion of individuals who
who ran the stop sign was independent of the type of vehicle driven and that you had rejected your
null hypothesis. Use a Marascuilo procedure to find the 6 possible differences between
proportions and to find out if there are any pairs of vehicle types where the difference between the
proportions is insignificant.
Note that in 1b) it says to assume that data have equal variances and in 3b) it says to
assume that the null hypothesis had been rejected. You do not get credit for testing
assumptions if it is not offered.
1
252y0621s1 11/4/06
Worksheet for Problem III – 1
————— 10/30/2006 9:43:16 PM ————————————————————
Welcome to Minitab, press F1 for help.
MTB > WOpen "C:\Documents and Settings\RBOVE\My Documents\Minitab\252x0602101.MTW".
Retrieving worksheet from file: 'C:\Documents and Settings\RBOVE\My
Documents\Minitab\252x06021-01.MTW'
Worksheet was saved on Mon Oct 30 2006
Results for: 252x06021-01.MTW
#times for all 11 tellers
MTB > print c1-c11
Data Display
Row
1
2
3
4
5
6
7
8
9
10
11
12
13
14
tel 1
2.9
3.9
2.6
3.1
3.9
2.6
3.3
3.0
3.5
3.1
3.2
2.4
4.0
4.3
tel 2
2.8
2.6
2.6
2.9
2.9
2.8
2.3
2.4
2.0
2.5
2.4
2.0
4.1
4.3
Row
1
2
3
4
5
6
7
8
9
10
11
12
13
14
tel 11
3.4
4.4
3.1
3.6
4.4
3.1
3.8
3.5
4.0
3.6
3.7
2.9
4.5
4.8
tel 3
2.6
2.7
3.2
2.8
3.6
2.1
2.3
2.6
2.6
2.9
2.4
2.3
0.5
4.7
tel 4
7.7
2.9
4.3
2.7
3.4
4.4
5.5
3.4
3.4
3.5
4.0
3.4
4.1
3.8
tel 5
2.4
13.4
5.8
1.5
9.8
2.7
2.7
4.5
2.3
5.8
4.8
4.2
5.8
6.1
tel 6
6.6
3.7
9.7
1.9
10.1
4.5
2.9
9.9
3.0
31.5
3.5
5.3
9.8
5.3
tel 7
3.5
8.4
4.3
3.3
11.9
3.7
3.0
2.9
3.6
5.4
4.4
3.0
4.3
5.4
tel 8
3.4
8.3
4.2
3.2
11.0
3.6
2.9
2.8
3.5
5.3
4.3
2.9
4.2
5.3
tel 9
3.5
3.4
3.8
3.4
3.6
3.5
4.8
3.5
5.3
3.7
3.4
3.6
3.8
3.8
tel 10
2.3
6.9
3.3
5.3
3.0
3.3
6.1
3.1
2.6
4.4
15.0
6.9
2.1
10.4
MTB > describe c1 - c11
Descriptive Statistics: tel 1, tel 2, tel 3, tel 4, tel 5, tel 6, tel 7, ...
Variable
tel 1
tel 2
tel 3
tel 4
tel 5
N
14
14
14
14
14
N*
0
0
0
0
0
Mean
3.271
2.757
2.664
4.036
5.129
SE Mean
0.155
0.181
0.243
0.338
0.859
StDev
0.580
0.677
0.909
1.265
3.214
Minimum
2.400
2.000
0.500
2.700
1.500
Q1
2.825
2.375
2.300
3.400
2.625
Median
3.150
2.600
2.600
3.650
4.650
Q3
3.900
2.900
2.975
4.325
5.875
Maximum
4.300
4.300
4.700
7.700
13.400
2
252y0621s1 11/4/06
tel
tel
tel
tel
tel
tel
6
7
8
9
10
11
14
14
14
14
14
14
0
0
0
0
0
0
7.69
4.793
4.636
3.793
5.336
3.771
1.99
0.669
0.623
0.150
0.970
0.155
7.45
2.503
2.331
0.561
3.630
0.580
1.90
2.900
2.800
3.400
2.100
2.900
3.38
3.225
3.125
3.475
2.900
3.325
5.30
4.000
3.900
3.600
3.850
3.650
9.83
5.400
5.300
3.800
6.900
4.400
31.50
11.900
11.000
5.300
15.000
4.800
#Ranks of data within columns
MTB > print c21 - c31
Data Display
Row
1
2
3
4
5
6
7
8
9
10
11
12
13
14
C21
4.0
11.5
2.5
6.5
11.5
2.5
9.0
5.0
10.0
6.5
8.0
1.0
13.0
14.0
C22
9.5
7.5
7.5
11.5
11.5
9.5
3.0
4.5
1.5
6.0
4.5
1.5
13.0
14.0
C23
7.0
9.0
12.0
10.0
13.0
2.0
3.5
7.0
7.0
11.0
5.0
3.5
1.0
14.0
C24
14.0
2.0
11.0
1.0
4.5
12.0
13.0
4.5
4.5
7.0
9.0
4.5
10.0
8.0
C25
3.0
14.0
10.0
1.0
13.0
4.5
4.5
7.0
2.0
10.0
8.0
6.0
10.0
12.0
C26
9.0
5.0
10.0
1.0
13.0
6.0
2.0
12.0
3.0
14.0
4.0
7.5
11.0
7.5
C27
5.0
13.0
8.5
4.0
14.0
7.0
2.5
1.0
6.0
11.5
10.0
2.5
8.5
11.5
C28
5.0
13.0
8.5
4.0
14.0
7.0
2.5
1.0
6.0
11.5
10.0
2.5
8.5
11.5
C29
5.0
2.0
11.0
2.0
7.5
5.0
13.0
5.0
14.0
9.0
2.0
7.5
11.0
11.0
C30
2.0
11.5
6.5
9.0
4.0
6.5
10.0
5.0
3.0
8.0
14.0
11.5
1.0
13.0
C31
4.0
11.5
2.5
6.5
11.5
2.5
9.0
5.0
10.0
6.5
8.0
1.0
13.0
14.0
#data stacked together
MTB > print c32-c41
Data Display
Row
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
C32
2.9
3.9
2.6
3.1
3.9
2.6
3.3
3.0
3.5
3.1
3.2
2.4
4.0
4.3
2.8
2.6
2.6
2.9
2.9
2.8
2.3
2.4
2.0
2.5
2.4
2.0
4.1
4.3
C33
2.9
3.9
2.6
3.1
3.9
2.6
3.3
3.0
3.5
3.1
3.2
2.4
4.0
4.3
2.6
2.7
3.2
2.8
3.6
2.1
2.3
2.6
2.6
2.9
2.4
2.3
0.5
4.7
C34
2.9
3.9
2.6
3.1
3.9
2.6
3.3
3.0
3.5
3.1
3.2
2.4
4.0
4.3
7.7
2.9
4.3
2.7
3.4
4.4
5.5
3.4
3.4
3.5
4.0
3.4
4.1
3.8
C35
2.9
3.9
2.6
3.1
3.9
2.6
3.3
3.0
3.5
3.1
3.2
2.4
4.0
4.3
2.4
13.4
5.8
1.5
9.8
2.7
2.7
4.5
2.3
5.8
4.8
4.2
5.8
6.1
C36
2.9
3.9
2.6
3.1
3.9
2.6
3.3
3.0
3.5
3.1
3.2
2.4
4.0
4.3
6.6
3.7
9.7
1.9
10.1
4.5
2.9
9.9
3.0
31.5
3.5
5.3
9.8
5.3
C37
2.9
3.9
2.6
3.1
3.9
2.6
3.3
3.0
3.5
3.1
3.2
2.4
4.0
4.3
3.5
8.4
4.3
3.3
11.9
3.7
3.0
2.9
3.6
5.4
4.4
3.0
4.3
5.4
C38
2.9
3.9
2.6
3.1
3.9
2.6
3.3
3.0
3.5
3.1
3.2
2.4
4.0
4.3
3.4
8.3
4.2
3.2
11.0
3.6
2.9
2.8
3.5
5.3
4.3
2.9
4.2
5.3
C39
2.9
3.9
2.6
3.1
3.9
2.6
3.3
3.0
3.5
3.1
3.2
2.4
4.0
4.3
3.5
3.4
3.8
3.4
3.6
3.5
4.8
3.5
5.3
3.7
3.4
3.6
3.8
3.8
C40
2.9
3.9
2.6
3.1
3.9
2.6
3.3
3.0
3.5
3.1
3.2
2.4
4.0
4.3
2.3
6.9
3.3
5.3
3.0
3.3
6.1
3.1
2.6
4.4
15.0
6.9
2.1
10.4
C41
2.9
3.9
2.6
3.1
3.9
2.6
3.3
3.0
3.5
3.1
3.2
2.4
4.0
4.3
3.4
4.4
3.1
3.6
4.4
3.1
3.8
3.5
4.0
3.6
3.7
2.9
4.5
4.8
3
252y0621s1 11/4/06
#ranks of stacked data
MTB > print c52 - c61
Data Display
Row
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
C52
15.0
23.5
9.5
18.5
23.5
9.5
21.0
17.0
22.0
18.5
20.0
5.0
25.0
27.5
12.5
9.5
9.5
15.0
15.0
12.5
3.0
5.0
1.5
7.0
5.0
1.5
26.0
27.5
C53
14.5
24.5
9.0
17.5
24.5
9.0
21.0
16.0
22.0
17.5
19.5
5.5
26.0
27.0
9.0
12.0
19.5
13.0
23.0
2.0
3.5
9.0
9.0
14.5
5.5
3.5
1.0
28.0
C54
5.5
19.5
2.5
8.5
19.5
2.5
11.0
7.0
16.5
8.5
10.0
1.0
21.5
24.5
28.0
5.5
24.5
4.0
13.5
26.0
27.0
13.5
13.5
16.5
21.5
13.5
23.0
18.0
C55
9.0
16.5
5.5
11.5
16.5
5.5
14.0
10.0
15.0
11.5
13.0
3.5
18.0
20.0
3.5
28.0
24.0
1.0
27.0
7.5
7.5
21.0
2.0
24.0
22.0
19.0
24.0
26.0
C56
5.5
16.5
3.5
9.5
16.5
3.5
12.0
7.5
13.5
9.5
11.0
2.0
18.0
19.0
23.0
15.0
24.0
1.0
27.0
20.0
5.5
26.0
7.5
28.0
13.5
21.5
25.0
21.5
C57
4.5
18.5
2.5
9.5
18.5
2.5
12.5
7.0
14.5
9.5
11.0
1.0
20.0
22.0
14.5
27.0
22.0
12.5
28.0
17.0
7.0
4.5
16.0
25.5
24.0
7.0
22.0
25.5
C58
6.0
18.5
2.5
9.5
18.5
2.5
13.0
8.0
15.5
9.5
11.5
1.0
20.0
23.5
14.0
27.0
21.5
11.5
28.0
17.0
6.0
4.0
15.5
25.5
23.5
6.0
21.5
25.5
C59
4.0
23.5
2.5
6.5
23.5
2.5
9.0
5.0
14.5
6.5
8.0
1.0
25.0
26.0
14.5
11.0
21.0
11.0
17.5
14.5
27.0
14.5
28.0
19.0
11.0
17.5
21.0
21.0
C60
7.0
18.5
5.0
11.0
18.5
5.0
15.0
8.5
17.0
11.0
13.0
3.0
20.0
21.0
2.0
25.5
15.0
23.0
8.5
15.0
24.0
11.0
5.0
22.0
28.0
25.5
1.0
27.0
C61
4.5
20.5
2.5
8.5
20.5
2.5
12.0
6.0
14.5
8.5
11.0
1.0
22.5
24.0
13.0
25.5
8.5
16.5
25.5
8.5
19.0
14.5
22.5
16.5
18.0
4.5
27.0
28.0
#ranks of numbers in C2-11 relative to ranks on column 1.
MTB > print c62-c71
Data Display
Row
1
2
3
4
5
6
7
8
9
10
11
12
13
14
MTB
MTB
MTB
MTB
MTB
MTB
MTB
MTB
MTB
C62
12.5
9.5
9.5
15.0
15.0
12.5
3.0
5.0
1.5
7.0
5.0
1.5
26.0
27.5
>
>
>
>
>
>
>
>
>
let
let
let
let
let
let
let
let
let
C63
9.0
12.0
19.5
13.0
23.0
2.0
3.5
9.0
9.0
14.5
5.5
3.5
1.0
28.0
k62
k63
k64
k65
k66
k67
k68
k69
k70
=
=
=
=
=
=
=
=
=
C64
28.0
5.5
24.5
4.0
13.5
26.0
27.0
13.5
13.5
16.5
21.5
13.5
23.0
18.0
C65
3.5
28.0
24.0
1.0
27.0
7.5
7.5
21.0
2.0
24.0
22.0
19.0
24.0
26.0
C66
23.0
15.0
24.0
1.0
27.0
20.0
5.5
26.0
7.5
28.0
13.5
21.5
25.0
21.5
C67
14.5
27.0
22.0
12.5
28.0
17.0
7.0
4.5
16.0
25.5
24.0
7.0
22.0
25.5
C68
14.0
27.0
21.5
11.5
28.0
17.0
6.0
4.0
15.5
25.5
23.5
6.0
21.5
25.5
C69
14.5
11.0
21.0
11.0
17.5
14.5
27.0
14.5
28.0
19.0
11.0
17.5
21.0
21.0
C70
2.0
25.5
15.0
23.0
8.5
15.0
24.0
11.0
5.0
22.0
28.0
25.5
1.0
27.0
C71
13.0
25.5
8.5
16.5
25.5
8.5
19.0
14.5
22.5
16.5
18.0
4.5
27.0
28.0
sum(c62)
sum(c63)
sum(c64)
sum(c65)
sum(c66)
sum(c67)
sum(c68)
sum(c69)
sum(c70)
4
252y0621s1 11/4/06
MTB > let k71 = sum(c71)
#Column sums
MTB > print k62-k71
Data Display
K62
K63
K64
K65
K66
K67
K68
K69
K70
K71
150.500
152.500
248.000
236.500
258.500
252.500
246.500
248.500
232.500
247.500
5
252y0621s1 11/4/06
Takehome Problem 1 Version 2
MTB > normtest c2;
SUBC> kstest.
Probability Plot of tel 2
MTB > VarTest c1 c2;
SUBC>
Unstacked.
Test for Equal Variances: tel 1, tel 2
95% Bonferroni confidence intervals for standard deviations
N
Lower
StDev
Upper
tel 1 14 0.402354 0.579693 1.00741
tel 2 14 0.469736 0.676773 1.17612
F-Test (normal distribution)
Test statistic = 0.73, p-value = 0.585
Levene's Test (any continuous distribution)
Test statistic = 0.01, p-value = 0.933
Test for Equal Variances for tel 1, tel 2
6
252y0621s1 11/4/06
MTB > TwoSample c1 c2.
Two-Sample T-Test and CI: tel 1, tel 2
Two-sample T for tel 1 vs tel 2
N
Mean StDev SE Mean
tel 1 14 3.271 0.580
0.15
tel 2 14 2.757 0.677
0.18
Difference = mu (tel 1) - mu (tel 2)
Estimate for difference: 0.514286
95% CI for difference: (0.023791, 1.004780)
T-Test of difference = 0 (vs not =): T-Value = 2.16
P-Value = 0.041
DF = 25
P-Value = 0.040
DF = 26
MTB > TwoSample c1 c2;
SUBC>
Pooled.
Two-Sample T-Test and CI: tel 1, tel 2
Two-sample T for tel 1 vs tel 2
N
Mean StDev SE Mean
tel 1 14 3.271 0.580
0.15
tel 2 14 2.757 0.677
0.18
Difference = mu (tel 1) - mu (tel 2)
Estimate for difference: 0.514286
95% CI for difference: (0.024746, 1.003825)
T-Test of difference = 0 (vs not =): T-Value = 2.16
Both use Pooled StDev = 0.6301
7
252y0621s1 11/4/06
MTB > Mann-Whitney 95.0 c1
SUBC>
Alternative 0.
c2;
Mann-Whitney Test and CI: tel 1, tel 2
tel 1
tel 2
N
14
14
Median
3.1500
2.6000
Point estimate for ETA1-ETA2 is 0.6000
95.4 Percent CI for ETA1-ETA2 is (0.0999,1.1000)
W = 255.5
Test of ETA1 = ETA2 vs ETA1 not = ETA2 is significant at 0.0169
The test is significant at 0.0165 (adjusted for ties)
8
252y0621s1 11/4/06
Takehome Problem 1 Version 3
MTB > normtest c3;
SUBC> kstest.
Probability Plot of tel 3
MTB > VarTest c1 c3;
SUBC>
Unstacked.
Test for Equal Variances: tel 1, tel 3
95% Bonferroni confidence intervals for standard deviations
tel 1
tel 3
N
14
14
Lower
0.402354
0.630641
StDev
0.579693
0.908598
Upper
1.00741
1.57900
F-Test (normal distribution)
Test statistic = 0.41, p-value = 0.118
Levene's Test (any continuous distribution)
Test statistic = 0.19, p-value = 0.665
Test for Equal Variances for tel 1, tel 3
MTB > TwoSample c1 c3.
Two-Sample T-Test and CI: tel 1, tel 3
Two-sample T for tel 1 vs tel 3
N
Mean StDev SE Mean
tel 1 14 3.271 0.580
0.15
tel 3 14 2.664 0.909
0.24
Difference = mu (tel 1) - mu (tel 3)
Estimate for difference: 0.607143
95% CI for difference: (0.009770, 1.204515)
T-Test of difference = 0 (vs not =): T-Value = 2.11
P-Value = 0.047
DF = 22
9
252y0621s1 11/4/06
MTB > TwoSample c1 c3;
SUBC>
Pooled.
Two-Sample T-Test and CI: tel 1, tel 3
Two-sample T for tel 1 vs tel 3
N
Mean StDev SE Mean
tel 1 14 3.271 0.580
0.15
tel 3 14 2.664 0.909
0.24
Difference = mu (tel 1) - mu (tel 3)
Estimate for difference: 0.607143
95% CI for difference: (0.015054, 1.199232)
T-Test of difference = 0 (vs not =): T-Value = 2.11
Both use Pooled StDev = 0.7621
MTB > Mann-Whitney 95.0 c1
SUBC>
Alternative 0.
P-Value = 0.045
DF = 26
c3;
Mann-Whitney Test and CI: tel 1, tel 3
N Median
tel 1 14
3.150
tel 3 14
2.600
Point estimate for ETA1-ETA2 is 0.600
95.4 Percent CI for ETA1-ETA2 is (0.100,1.100)
W = 253.5
Test of ETA1 = ETA2 vs ETA1 not = ETA2 is significant at 0.0216
The test is significant at 0.0211 (adjusted for ties)
10
252y0621s1 11/4/06
Takehome Problem 1 Version 4
MTB > normtest c4;
SUBC> kstest.
Probability Plot of tel 4
MTB > VarTest c1 c4;
SUBC>
Unstacked.
Test for Equal Variances: tel 1, tel 4
95% Bonferroni confidence intervals for standard deviations
N
Lower
StDev
Upper
tel 1 14 0.402354 0.57969 1.00741
tel 4 14 0.878207 1.26528 2.19886
F-Test (normal distribution)
Test statistic = 0.21, p-value = 0.008
Levene's Test (any continuous distribution)
Test statistic = 1.30, p-value = 0.264
Test for Equal Variances for tel 1, tel 4
MTB > TwoSample c1 c4.
Two-Sample T-Test and CI: tel 1, tel 4
Two-sample T for tel 1 vs tel 4
N
Mean StDev SE Mean
tel 1 14 3.271 0.580
0.15
tel 4 14
4.04
1.27
0.34
Difference = mu (tel 1) - mu (tel 4)
Estimate for difference: -0.764286
95% CI for difference: (-1.545748, 0.017177)
T-Test of difference = 0 (vs not =): T-Value = -2.05
P-Value = 0.055
DF = 18
11
252y0621s1 11/4/06
MTB > TwoSample c1 c4;
SUBC>
Pooled.
Two-Sample T-Test and CI: tel 1, tel 4
Two-sample T for tel 1 vs tel 4
N
Mean StDev SE Mean
tel 1 14 3.271 0.580
0.15
tel 4 14
4.04
1.27
0.34
Difference = mu (tel 1) - mu (tel 4)
Estimate for difference: -0.764286
95% CI for difference: (-1.528864, 0.000293)
T-Test of difference = 0 (vs not =): T-Value = -2.05
Both use Pooled StDev = 0.9841
MTB > Mann-Whitney 95.0 c1
SUBC>
Alternative 0.
P-Value = 0.050
DF = 26
c4;
Mann-Whitney Test and CI: tel 1, tel 4
tel 1
tel 4
N
14
14
Median
3.150
3.650
Point estimate for ETA1-ETA2 is -0.500
95.4 Percent CI for ETA1-ETA2 is (-1.100,-0.000)
W = 158.0
Test of ETA1 = ETA2 vs ETA1 not = ETA2 is significant at 0.0409
The test is significant at 0.0404 (adjusted for ties)
12
252y0621s1 11/4/06
Takehome Problem 1 Version 5
MTB > normtest c5;
SUBC> kstest.
Probability Plot of tel 5
MTB > VarTest c1 c5;
SUBC>
Unstacked.
Test for Equal Variances: tel 1, tel 5
95% Bonferroni confidence intervals for standard deviations
tel 1
tel 5
N
14
14
Lower
0.40235
2.23095
StDev
0.57969
3.21425
Upper
1.00741
5.58587
F-Test (normal distribution)
Test statistic = 0.03, p-value = 0.000
Levene's Test (any continuous distribution)
Test statistic = 8.20, p-value = 0.008
Test for Equal Variances for tel 1, tel 5
MTB > TwoSample c1 c5.
Two-Sample T-Test and CI: tel 1, tel 5
Two-sample T for tel 1 vs tel 5
N
Mean StDev SE Mean
tel 1 14 3.271 0.580
0.15
tel 5 14
5.13
3.21
0.86
Difference = mu (tel 1) - mu (tel 5)
Estimate for difference: -1.85714
95% CI for difference: (-3.74294, 0.02865)
T-Test of difference = 0 (vs not =): T-Value = -2.13
P-Value = 0.053
DF = 13
13
252y0621s1 11/4/06
MTB > TwoSample c1 c5;
SUBC>
Pooled.
Two-Sample T-Test and CI: tel 1, tel 5
Two-sample T for tel 1 vs tel 5
N
Mean StDev SE Mean
tel 1 14 3.271 0.580
0.15
tel 5 14
5.13
3.21
0.86
Difference = mu (tel 1) - mu (tel 5)
Estimate for difference: -1.85714
95% CI for difference: (-3.65142, -0.06286)
T-Test of difference = 0 (vs not =): T-Value = -2.13
Both use Pooled StDev = 2.3095
MTB > Mann-Whitney 95.0 c1
SUBC>
Alternative 0.
P-Value = 0.043
DF = 26
c5;
Mann-Whitney Test and CI: tel 1, tel 5
tel 1
tel 5
N
14
14
Median
3.150
4.650
Point estimate for ETA1-ETA2 is -1.500
95.4 Percent CI for ETA1-ETA2 is (-2.700,0.299)
W = 169.5
Test of ETA1 = ETA2 vs ETA1 not = ETA2 is significant at 0.1295
The test is significant at 0.1290 (adjusted for ties)
14
252y0621s1 11/4/06
Takehome Problem 1 Version 6
MTB > normtest c6;
SUBC> kstest.
Probability Plot of tel 6
MTB > VarTest c1 c6;
SUBC>
Unstacked.
Test for Equal Variances: tel 1, tel 6
95% Bonferroni confidence intervals for standard deviations
N
Lower
StDev
Upper
tel 1 14 0.40235 0.57969
1.0074
tel 6 14 5.16839 7.44637 12.9406
F-Test (normal distribution)
Test statistic = 0.01, p-value = 0.000
Levene's Test (any continuous distribution)
Test statistic = 4.42, p-value = 0.045
Test for Equal Variances for tel 1, tel 6
MTB > TwoSample c1 c6.
Two-Sample T-Test and CI: tel 1, tel 6
Two-sample T for tel 1 vs tel 6
N
Mean StDev SE Mean
tel 1 14 3.271 0.580
0.15
tel 6 14
7.69
7.45
2.0
Difference = mu (tel 1) - mu (tel 6)
Estimate for difference: -4.42143
95% CI for difference: (-8.73384, -0.10901)
T-Test of difference = 0 (vs not =): T-Value = -2.21
P-Value = 0.045
DF = 13
15
252y0621s1 11/4/06
MTB > TwoSample c1 c6;
SUBC>
Pooled.
Two-Sample T-Test and CI: tel 1, tel 6
Two-sample T for tel 1 vs tel 6
N
Mean StDev SE Mean
tel 1 14 3.271 0.580
0.15
tel 6 14
7.69
7.45
2.0
Difference = mu (tel 1) - mu (tel 6)
Estimate for difference: -4.42143
95% CI for difference: (-8.52457, -0.31829)
T-Test of difference = 0 (vs not =): T-Value = -2.21
Both use Pooled StDev = 5.2813
MTB > Mann-Whitney 95.0 c1
SUBC>
Alternative 0.
P-Value = 0.036
DF = 26
c6;
Mann-Whitney Test and CI: tel 1, tel 6
tel 1
tel 6
N
14
14
Median
3.150
5.300
Point estimate for ETA1-ETA2 is -2.150
95.4 Percent CI for ETA1-ETA2 is (-6.201,-0.400)
W = 147.5
Test of ETA1 = ETA2 vs ETA1 not = ETA2 is significant at 0.0115
The test is significant at 0.0114 (adjusted for ties)
16
252y0621s1 11/4/06
Takehome Problem 1 Version 7
MTB > normtest c7;
SUBC> kstest.
Probability Plot of tel 7
MTB > VarTest c1 c7;
SUBC>
Unstacked.
Test for Equal Variances: tel 1, tel 7
95% Bonferroni confidence intervals for standard deviations
N
Lower
StDev
Upper
tel 1 14 0.40235 0.57969 1.00741
tel 7 14 1.73712 2.50276 4.34940
F-Test (normal distribution)
Test statistic = 0.05, p-value = 0.000
Levene's Test (any continuous distribution)
Test statistic = 3.34, p-value = 0.079
Test for Equal Variances for tel 1, tel 7
MTB > TwoSample c1 c7.
Two-Sample T-Test and CI: tel 1, tel 7
Two-sample T for tel 1 vs tel 7
N
Mean StDev SE Mean
tel 1 14 3.271 0.580
0.15
tel 7 14
4.79
2.50
0.67
Difference = mu (tel 1) - mu (tel 7)
Estimate for difference: -1.52143
95% CI for difference: (-2.99403, -0.04882)
T-Test of difference = 0 (vs not =): T-Value = -2.22
P-Value = 0.044
DF = 14
17
252y0621s1 11/4/06
MTB > TwoSample c1 c7;
SUBC>
Pooled.
Two-Sample T-Test and CI: tel 1, tel 7
Two-sample T for tel 1 vs tel 7
N
Mean StDev SE Mean
tel 1 14 3.271 0.580
0.15
tel 7 14
4.79
2.50
0.67
Difference = mu (tel 1) - mu (tel 7)
Estimate for difference: -1.52143
95% CI for difference: (-2.93275, -0.11011)
T-Test of difference = 0 (vs not =): T-Value = -2.22
Both use Pooled StDev = 1.8166
MTB > Mann-Whitney 95.0 c1
SUBC>
Alternative 0.
P-Value = 0.036
DF = 26
c7;
Mann-Whitney Test and CI: tel 1, tel 7
tel 1
tel 7
N
14
14
Median
3.150
4.000
Point estimate for ETA1-ETA2 is -0.700
95.4 Percent CI for ETA1-ETA2 is (-1.700,-0.099)
W = 153.5
Test of ETA1 = ETA2 vs ETA1 not = ETA2 is significant at 0.0244
The test is significant at 0.0241 (adjusted for ties)
18
252y0621s1 11/4/06
Takehome Problem 1 Version 8
MTB > normtest c8;
SUBC> kstest.
Probability Plot of tel 8
MTB > VarTest c1 c8;
SUBC>
Unstacked.
Test for Equal Variances: tel 1, tel 8
95% Bonferroni confidence intervals for standard deviations
N
Lower
StDev
Upper
tel 1 14 0.40235 0.57969 1.00741
tel 8 14 1.61808 2.33126 4.05136
F-Test (normal distribution)
Test statistic = 0.06, p-value = 0.000
Levene's Test (any continuous distribution)
Test statistic = 3.56, p-value = 0.071
Test for Equal Variances for tel 1, tel 8
MTB > TwoSample c1 c8.
Two-Sample T-Test and CI: tel 1, tel 8
Two-sample T for tel 1 vs tel 8
N
Mean StDev SE Mean
tel 1 14 3.271 0.580
0.15
tel 8 14
4.64
2.33
0.62
Difference = mu (tel 1) - mu (tel 8)
Estimate for difference: -1.36429
95% CI for difference: (-2.74130, 0.01273)
T-Test of difference = 0 (vs not =): T-Value = -2.12
P-Value = 0.052
DF = 14
19
252y0621s1 11/4/06
MTB > TwoSample c1 c8;
SUBC>
Pooled.
Two-Sample T-Test and CI: tel 1, tel 8
Two-sample T for tel 1 vs tel 8
N
Mean StDev SE Mean
tel 1 14 3.271 0.580
0.15
tel 8 14
4.64
2.33
0.62
Difference = mu (tel 1) - mu (tel 8)
Estimate for difference: -1.36429
95% CI for difference: (-2.68400, -0.04458)
T-Test of difference = 0 (vs not =): T-Value = -2.12
Both use Pooled StDev = 1.6987
MTB > Mann-Whitney 95.0 c1
SUBC>
Alternative 0.
P-Value = 0.043
DF = 26
c8;
Mann-Whitney Test and CI: tel 1, tel 8
N Median
tel 1 14
3.150
tel 8 14
3.900
Point estimate for ETA1-ETA2 is -0.600
95.4 Percent CI for ETA1-ETA2 is (-1.599,-0.000)
W = 159.5
Test of ETA1 = ETA2 vs ETA1 not = ETA2 is significant at 0.0482
The test is significant at 0.0478 (adjusted for ties)
20
252y0621s1 11/4/06
Takehome Problem 1 Version 9
MTB > normtest c9;
SUBC> kstest.
Probability Plot of tel 9
MTB > VarTest c1 c9;
SUBC>
Unstacked.
Test for Equal Variances: tel 1, tel 9
95% Bonferroni confidence intervals for standard deviations
N
Lower
StDev
Upper
tel 1 14 0.402354 0.579693 1.00741
tel 9 14 0.389280 0.560857 0.97468
F-Test (normal distribution)
Test statistic = 1.07, p-value = 0.907
Levene's Test (any continuous distribution)
Test statistic = 0.70, p-value = 0.412
Test for Equal Variances for tel 1, tel 9
MTB > TwoSample c1 c9.
Two-Sample T-Test and CI: tel 1, tel 9
Two-sample T for tel 1 vs tel 9
N
Mean StDev SE Mean
tel 1 14 3.271 0.580
0.15
tel 9 14 3.793 0.561
0.15
Difference = mu (tel 1) - mu (tel 9)
Estimate for difference: -0.521429
95% CI for difference: (-0.965410, -0.077448)
T-Test of difference = 0 (vs not =): T-Value = -2.42
P-Value = 0.023
DF = 25
21
252y0621s1 11/4/06
MTB > TwoSample c1 c9;
SUBC>
Pooled.
Two-Sample T-Test and CI: tel 1, tel 9
Two-sample T for tel 1 vs tel 9
N
Mean StDev SE Mean
tel 1 14 3.271 0.580
0.15
tel 9 14 3.793 0.561
0.15
Difference = mu (tel 1) - mu (tel 9)
Estimate for difference: -0.521429
95% CI for difference: (-0.964545, -0.078312)
T-Test of difference = 0 (vs not =): T-Value = -2.42
Both use Pooled StDev = 0.5704
MTB > Mann-Whitney 95.0 c1
SUBC>
Alternative 0.
P-Value = 0.023
DF = 26
c9;
Mann-Whitney Test and CI: tel 1, tel 9
tel 1
tel 9
N
14
14
Median
3.1500
3.6000
Point estimate for ETA1-ETA2 is -0.5000
95.4 Percent CI for ETA1-ETA2 is (-0.9001,-0.1000)
W = 157.5
Test of ETA1 = ETA2 vs ETA1 not = ETA2 is significant at 0.0387
The test is significant at 0.0381 (adjusted for ties)
22
252y0621s1 11/4/06
Takehome Problem 1 Version 10
MTB > normtest c10;
SUBC> kstest.
Probability Plot of tel 10
MTB > VarTest c1 c10;
SUBC>
Unstacked.
Test for Equal Variances: tel 1, tel 10
95% Bonferroni confidence intervals for standard deviations
N
Lower
StDev
Upper
tel 1 14 0.40235 0.57969 1.00741
tel 10 14 2.51961 3.63013 6.30860
F-Test (normal distribution)
Test statistic = 0.03, p-value = 0.000
Levene's Test (any continuous distribution)
Test statistic = 6.75, p-value = 0.015
Test for Equal Variances for tel 1, tel 10
MTB > TwoSample c1 c10.
Two-Sample T-Test and CI: tel 1, tel 10
Two-sample T for tel 1 vs tel 10
N
Mean StDev SE Mean
tel 1
14 3.271 0.580
0.15
tel 10 14
5.34
3.63
0.97
Difference = mu (tel 1) - mu (tel 10)
Estimate for difference: -2.06429
95% CI for difference: (-4.18682, 0.05825)
T-Test of difference = 0 (vs not =): T-Value = -2.10
P-Value = 0.056
DF = 13
23
252y0621s1 11/4/06
MTB > TwoSample c1 c10;
SUBC>
Pooled.
Two-Sample T-Test and CI: tel 1, tel 10
Two-sample T for tel 1 vs tel 10
N
Mean StDev SE Mean
tel 1
14 3.271 0.580
0.15
tel 10 14
5.34
3.63
0.97
Difference = mu (tel 1) - mu (tel 10)
Estimate for difference: -2.06429
95% CI for difference: (-4.08381, -0.04476)
T-Test of difference = 0 (vs not =): T-Value = -2.10
Both use Pooled StDev = 2.5994
MTB > Mann-Whitney 95.0 c1
SUBC>
Alternative 0.
P-Value = 0.045
DF = 26
c10;
Mann-Whitney Test and CI: tel 1, tel 10
tel 1
tel 10
N
14
14
Median
3.150
3.850
Point estimate for ETA1-ETA2 is -0.700
95.4 Percent CI for ETA1-ETA2 is (-3.000,0.301)
W = 173.5
Test of ETA1 = ETA2 vs ETA1 not = ETA2 is significant at 0.1827
The test is significant at 0.1818 (adjusted for ties)
24
252y0621s1 11/4/06
Takehome Problem 1 Version 11
MTB > normtest c11;
SUBC> kstest.
Probability Plot of tel 11
MTB > VarTest c1 c11;
SUBC>
Unstacked.
Test for Equal Variances: tel 1, tel 11
95% Bonferroni confidence intervals for standard deviations
N
Lower
StDev
Upper
tel 1 14 0.402354 0.579693 1.00741
tel 11 14 0.402354 0.579693 1.00741
F-Test (normal distribution)
Test statistic = 1.00, p-value = 1.000
Levene's Test (any continuous distribution)
Test statistic = 0.00, p-value = 1.000
Test for Equal Variances for tel 1, tel 11
MTB > TwoSample c1 c11.
Two-Sample T-Test and CI: tel 1, tel 11
Two-sample T for tel 1 vs tel 11
N
Mean StDev SE Mean
tel 1
14 3.271 0.580
0.15
tel 11 14 3.771 0.580
0.15
Difference = mu (tel 1) - mu (tel 11)
Estimate for difference: -0.500000
95% CI for difference: (-0.950373, -0.049627)
T-Test of difference = 0 (vs not =): T-Value = -2.28
P-Value = 0.031
DF = 26
25
252y0621s1 11/4/06
MTB > TwoSample c1 c11;
SUBC>
Pooled.
Two-Sample T-Test and CI: tel 1, tel 11
Two-sample T for tel 1 vs tel 11
N
Mean StDev SE Mean
tel 1
14 3.271 0.580
0.15
tel 11 14 3.771 0.580
0.15
Difference = mu (tel 1) - mu (tel 11)
Estimate for difference: -0.500000
95% CI for difference: (-0.950373, -0.049627)
T-Test of difference = 0 (vs not =): T-Value = -2.28
Both use Pooled StDev = 0.5797
MTB > Mann-Whitney 95.0 c1
SUBC>
Alternative 0.
P-Value = 0.031
DF = 26
c11;
Mann-Whitney Test and CI: tel 1, tel 11
N Median
tel 1
14 3.1500
tel 11 14 3.6500
Point estimate for ETA1-ETA2 is -0.5000
95.4 Percent CI for ETA1-ETA2 is (-0.9997,-0.0003)
W = 158.5
Test of ETA1 = ETA2 vs ETA1 not = ETA2 is significant at 0.0432
The test is significant at 0.0427 (adjusted for ties)
26
252y0621s1 11/4/06
Variance computations.Computer aided.
Worksheet was saved on Tue Oct 31 2006
Results for: 252x06021-01.MTW Computation of variance for version 9
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let c16 = c6
let c12 = c9
let c14 = c12 - mean(c12)
let c15 = c14*c14
name k12 'sumx9'
name k13 'sumx9sq'
name k14 'sumx9^'
name k15 'sumx9^sq'
let k12 = sum (c12)
let k13 = sum(c13)
let k15 = sum(c15)
let k14 = sum(c14)
name k112 'meanx9'
name k113 'denx9'
name k114 'var1x9'
name k115 'var2x9'
let k112 = k12/14
let k113 = 14*k112*k112
let k113 = k13-k113
let k114 = k113/13
let k115 = k15/13
print c12 - c15
Data Display
Row
1
2
3
4
5
6
7
8
9
10
11
12
13
14
x9
3.5
3.4
3.8
3.4
3.6
3.5
4.8
3.5
5.3
3.7
3.4
3.6
3.8
3.8
x9sq
12.25
11.56
14.44
11.56
12.96
12.25
23.04
12.25
28.09
13.69
11.56
12.96
14.44
14.44
x9^
-0.29286
-0.39286
0.00714
-0.39286
-0.19286
-0.29286
1.00714
-0.29286
1.50714
-0.09286
-0.39286
-0.19286
0.00714
0.00714
x9^sq
0.08577
0.15434
0.00005
0.15434
0.03719
0.08577
1.01434
0.08577
2.27148
0.00862
0.15434
0.03719
0.00005
0.00005
MTB > print k12 - k15
Data Display
sumx9
sumx9sq
sumx9^
sumx9^sq
53.1000
205.490
-0.000000000
4.08929
MTB > print k112 - k115
Data Display
meanx9
denx9
var1x9
var2x9
MTB > let
3.79286
4.08929
0.314560
0.314560
denx9 = sqrt(k114)
MTB > print denx9
Data Display
denx9
0.560857
27
252y0621s1 11/4/06
Computation of variance for version 6
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let c16 = c6
let c17 = c16*c16
let c18=c16- mean(c16)
let c19= c18*c18
name k16 'sumx6'
name k17 'sumx6sq'
name k18 'sumx6^'
name k19 'sumx6^sq'
let k16 = sum (c16)
let k17 = sum(c17)
let k18 = sum(c18)
let k19 = sum(c19)
name k116 'meanx6'
name k117 'denx6'
name k118 'var1x6'
name k119 'var2x6'
let k116 = k16/14
let k117 = 14*k116*k116
let k117 = k17-k117
let k118 = k117/13
let k119 = k19/13
print c16 - c19
Data Display
Row
1
2
3
4
5
6
7
8
9
10
11
12
13
14
x6
6.6
3.7
9.7
1.9
10.1
4.5
2.9
9.9
3.0
31.5
3.5
5.3
9.8
5.3
x6sq
43.56
13.69
94.09
3.61
102.01
20.25
8.41
98.01
9.00
992.25
12.25
28.09
96.04
28.09
x6^
-1.0929
-3.9929
2.0071
-5.7929
2.4071
-3.1929
-4.7929
2.2071
-4.6929
23.8071
-4.1929
-2.3929
2.1071
-2.3929
x6^sq
1.194
15.943
4.029
33.557
5.794
10.194
22.971
4.871
22.023
566.780
17.580
5.726
4.440
5.726
MTB > print k16 - k19
Data Display
sumx6
sumx6sq
sumx6^
sumx6^sq
107.700
1549.35
0.000000000
720.829
MTB > print k116 - k119
Data Display
meanx6
denx6
var1x6
var2x6
7.69286
720.829
55.4484
55.4484
MTB > let denx6 = sqrt(k118)
MTB > print denx6
Data Display
denx6
7.44637
28
252y0621s1 11/4/06
Lilliefors Computations – Version 4
MTB > WOpen "C:\Documents and Settings\RBOVE\My Documents\Minitab\252x0602101.MTW".
Retrieving worksheet from file: 'C:\Documents and Settings\RBOVE\My
Documents\Minitab\252x06021-01.MTW'
Worksheet was saved on Tue Oct 31 2006
Results for: 252x06021-01.MTW
MTB > New.
#
Results for: Worksheet 2
MTB > describe c1
Descriptive Statistics: x
Variable
x
N
14
N*
0
Mean
4.036
SE Mean
0.338
StDev
1.265
Minimum
2.700
Q1
3.400
Median
3.650
Q3
4.325
Maximum
7.700
MTB > let c2 = c1 - 4.036
MTB > sum c2
Sum of z
Sum of z = -0.00400000
#Just checking that 4.036 is close to the mean.
MTB > let c2 = c2/1.265
MTB > let c5 = c4/14
MTB > let c11 = c1
MTB >
SUBC>
MTB >
MTB >
SUBC>
#C1 and C2 were not in order so I moved them to C11
#and C12.
#Now I’m putting sorted columns into C1 and C2.
Sort C11 c1;
By C11.
let c12 = c2
sort c12 c2;
by c12.
MTB > CDF c2 c6;
SUBC>
Normal 0.0 1.0.
#Does the cumulative Normal distribution
MTB > let c7 = c5 - c6
MTB > print c1-c7
Data Display
Row
1
2
3
4
5
6
7
8
9
10
11
12
13
14
x
2.7
2.9
3.4
3.4
3.4
3.4
3.5
3.8
4.0
4.1
4.3
4.4
5.5
7.7
z
-1.05613
-0.89802
-0.50277
-0.50277
-0.50277
-0.50277
-0.42372
-0.18656
-0.02846
0.05059
0.20870
0.28775
1.15731
2.89644
O
1
1
1
1
1
1
1
1
1
1
1
1
1
1
FO
1
2
3
4
5
6
7
8
9
10
11
12
13
14
FO/n
0.07143
0.14286
0.21429
0.28571
0.35714
0.42857
0.50000
0.57143
0.64286
0.71429
0.78571
0.85714
0.92857
1.00000
Fz
0.145455
0.184586
0.307564
0.307564
0.307564
0.307564
0.335887
0.426002
0.488648
0.520175
0.582657
0.613230
0.876428
0.998113
D
-0.074027
-0.041729
-0.093278
-0.021850
0.049579
0.121007
0.164113
0.145426
0.154209
0.194111
0.203057
0.243913
0.052144
0.001887
29
252y0621s1 11/4/06
————— 11/3/2006 11:31:35 PM ————————————————————
Welcome to Minitab, press F1 for help.
MTB > echo
MTB > WOpen "C:\Documents and Settings\RBOVE\My Documents\Minitab\252x0602101.MTW".
Retrieving worksheet from file: 'C:\Documents and Settings\RBOVE\My
Documents\Minitab\252x06021-01.MTW'
Worksheet was saved on Tue Oct 31 2006
Results for: 252x060223-01.MTW
MTB > Execute "C:\Documents and Settings\RBOVE\My Documents\Minitab\252x062t3.mtb" 10.
Takehome Problem 3 Version 0
Executing from file: C:\Documents and Settings\RBOVE\My
Documents\Minitab\252x062-t3.mtb
MTB > #252062-t3 #Does last take-home problem
MTB > Name c1 'O11'
MTB > Name c2 'O21'
MTB > name c3 'O31'
MTB > name c4 'O41'
MTB > name c6 '012'
MTB > name C7 'O22'
MTB > name c8 'O32'
MTB > name c9 'O42'
MTB > name c11 'P1'
MTB > name c12 'P2'
MTB > name c13 'P3'
MTB > name c14 'P4'
MTB > let c11(1) = c6(2)/(c6(1)+c6(2))
MTB > let c12(1) = c7(2)/(c7(1)+c7(2))
MTB > let c13(1) = c8(2)/(c8(1)+c8(2))
MTB > let c14(1) = c9(2)/(c9(1)+c9(2))
MTB > let c11(2) = 1 - c11(1)
MTB > let c12(2) = 1 - c12(1)
MTB > let c13(2) = 1 - c13(1)
MTB > let c14(2) = 1 - c14(1)
MTB > Print c1-c4
Data Display
Row
1
2
3
O11
180
107
60
O21
24
18
8
O31
30
10
11
O41
14
20
16
30
252y0621s1 11/4/06
MTB > ChiSquare C1 C2 C3 C4
Chi-Square Test: O11, O21, O31, O41
Expected counts are printed below observed counts
Chi-Square contributions are printed below expected counts
O11
O21
O31
O41 Total
1
180
24
30
14
248
172.80 24.90 25.40 24.90
0.300 0.033 0.834 4.771
2
107
108.00
0.009
18
15.56
0.382
10
15.87
2.173
20
15.56
1.265
155
3
60
66.19
0.580
8
9.54
0.248
11
9.73
0.166
16
9.54
4.378
95
Total
347
50
51
50
498
Chi-Sq = 15.139, DF = 6, P-Value = 0.019
MTB > print c6-c9
Data Display
Row
1
2
012
287
60
O22
42
8
O32
40
11
O42
34
16
MTB > ChiSquare C6 C7 C8 C9
Chi-Square Test: 012, O22, O32, O42
Expected counts are printed below observed counts
Chi-Square contributions are printed below expected counts
012
O22
O32
O42 Total
1
287
42
40
34
403
280.81 40.46 41.27 40.46
0.137 0.058 0.039 1.032
2
60
66.19
0.580
8
9.54
0.248
11
9.73
0.166
16
9.54
4.378
95
Total
347
50
51
50
498
Chi-Sq = 6.638, DF = 3, P-Value = 0.084
MTB > print c11-c14
Data Display
Row
1
2
P1
0.172911
0.827089
P2
0.16
0.84
P3
0.215686
0.784314
P4
0.32
0.68
MTB > let c1(1) = c1(1) + 1
MTB > let c6(1) = c6(1) + 1
MTB > end
31
252y0621s1 11/4/06
Takehome Problem 3 Version 1
MTB
MTB
MTB
MTB
MTB
MTB
MTB
MTB
MTB
MTB
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MTB
MTB
MTB
MTB
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MTB
>
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#252062-t3 #Does last take-home problem
Name c1 'O11'
Name c2 'O21'
name c3 'O31'
name c4 'O41'
name c6 '012'
name C7 'O22'
name c8 'O32'
name c9 'O42'
name c11 'P1'
name c12 'P2'
name c13 'P3'
name c14 'P4'
let c11(1) = c6(2)/(c6(1)+c6(2))
let c12(1) = c7(2)/(c7(1)+c7(2))
let c13(1) = c8(2)/(c8(1)+c8(2))
let c14(1) = c9(2)/(c9(1)+c9(2))
let c11(2) = 1 - c11(1)
let c12(2) = 1 - c12(1)
let c13(2) = 1 - c13(1)
let c14(2) = 1 - c14(1)
Print c1-c4
Data Display
Row
1
2
3
O11
181
107
60
O21
24
18
8
O31
30
10
11
O41
14
20
16
MTB > ChiSquare C1 C2 C3 C4
Chi-Square Test: O11, O21, O31, O41
Expected counts are printed below observed counts
Chi-Square contributions are printed below expected counts
O11
181
173.65
0.311
O21
24
24.95
0.036
O31
30
25.45
0.814
O41
14
24.95
4.806
Total
249
2
107
108.10
0.011
18
15.53
0.392
10
15.84
2.154
20
15.53
1.286
155
3
60
66.25
0.590
8
9.52
0.242
11
9.71
0.172
16
9.52
4.413
95
Total
348
50
51
50
499
1
Chi-Sq = 15.227, DF = 6, P-Value = 0.019
MTB > print c6-c9
Data Display
Row
1
2
012
288
60
O22
42
8
O32
40
11
O42
34
16
32
252y0621s1 11/4/06
MTB > ChiSquare C6 C7 C8 C9
Chi-Square Test: 012, O22, O32, O42
Expected counts are printed below observed counts
Chi-Square contributions are printed below expected counts
1
2
012
288
281.75
0.139
O22
42
40.48
0.057
O32
40
41.29
0.040
O42
34
40.48
1.038
Total
404
60
66.25
0.590
8
9.52
0.242
11
9.71
0.172
16
9.52
4.413
95
Total
348
50
51
50
499
Chi-Sq = 6.690, DF = 3, P-Value = 0.082
MTB > print c11-c14
Data Display
Row
1
2
P1
0.172414
0.827586
P2
0.16
0.84
P3
0.215686
0.784314
P4
0.32
0.68
MTB > let c1(1) = c1(1) + 1
MTB > let c6(1) = c6(1) + 1
MTB > end
33
252y0621s1 11/4/06
Takehome Problem 3 Version 2
MTB
MTB
MTB
MTB
MTB
MTB
MTB
MTB
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MTB
MTB
MTB
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MTB
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#252062-t3 #Does last take-home problem
Name c1 'O11'
Name c2 'O21'
name c3 'O31'
name c4 'O41'
name c6 '012'
name C7 'O22'
name c8 'O32'
name c9 'O42'
name c11 'P1'
name c12 'P2'
name c13 'P3'
name c14 'P4'
let c11(1) = c6(2)/(c6(1)+c6(2))
let c12(1) = c7(2)/(c7(1)+c7(2))
let c13(1) = c8(2)/(c8(1)+c8(2))
let c14(1) = c9(2)/(c9(1)+c9(2))
let c11(2) = 1 - c11(1)
let c12(2) = 1 - c12(1)
let c13(2) = 1 - c13(1)
let c14(2) = 1 - c14(1)
MTB > Print c1-c4
Data Display
Row
1
2
3
O11
182
107
60
O21
24
18
8
O31
30
10
11
O41
14
20
16
MTB > ChiSquare C1 C2 C3 C4
Chi-Square Test: O11, O21, O31, O41
Expected counts are printed below observed counts
Chi-Square contributions are printed below expected counts
O11
182
174.50
0.322
O21
24
25.00
0.040
O31
30
25.50
0.794
O41
14
25.00
4.840
Total
250
2
107
108.19
0.013
18
15.50
0.403
10
15.81
2.135
20
15.50
1.306
155
3
60
66.31
0.600
8
9.50
0.237
11
9.69
0.177
16
9.50
4.447
95
Total
349
50
51
50
500
1
Chi-Sq = 15.316, DF = 6, P-Value = 0.018
MTB > print c6-c9
Data Display
Row
1
2
012
289
60
O22
42
8
O32
40
11
O42
34
16
34
252y0621s1 11/4/06
MTB > ChiSquare C6 C7 C8 C9
Chi-Square Test: 012, O22, O32, O42
Expected counts are printed below observed counts
Chi-Square contributions are printed below expected counts
012
289
282.69
0.141
O22
42
40.50
0.056
O32
40
41.31
0.042
O42
34
40.50
1.043
Total
405
2
60
66.31
0.600
8
9.50
0.237
11
9.69
0.177
16
9.50
4.447
95
Total
349
50
51
50
500
1
Chi-Sq = 6.743, DF = 3, P-Value = 0.081
MTB > print c11-c14
Data Display
Row
1
2
P1
0.171920
0.828080
P2
0.16
0.84
P3
0.215686
0.784314
P4
0.32
0.68
MTB > let c1(1) = c1(1) + 1
MTB > let c6(1) = c6(1) + 1
MTB > end
35
252y0621s1 11/4/06
Takehome Problem 3 Version 3
MTB
MTB
MTB
MTB
MTB
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#252062-t3 #Does last take-home problem
Name c1 'O11'
Name c2 'O21'
name c3 'O31'
name c4 'O41'
name c6 '012'
name C7 'O22'
name c8 'O32'
name c9 'O42'
name c11 'P1'
name c12 'P2'
name c13 'P3'
name c14 'P4'
let c11(1) = c6(2)/(c6(1)+c6(2))
let c12(1) = c7(2)/(c7(1)+c7(2))
let c13(1) = c8(2)/(c8(1)+c8(2))
let c14(1) = c9(2)/(c9(1)+c9(2))
let c11(2) = 1 - c11(1)
let c12(2) = 1 - c12(1)
let c13(2) = 1 - c13(1)
let c14(2) = 1 - c14(1)
MTB > Print c1-c4
Data Display
Row
1
2
3
O11
183
107
60
O21
24
18
8
O31
30
10
11
O41
14
20
16
MTB > ChiSquare C1 C2 C3 C4
Chi-Square Test: O11, O21, O31, O41
Expected counts are printed below observed counts
Chi-Square contributions are printed below expected counts
O11
183
175.35
0.334
O21
24
25.05
0.044
O31
30
25.55
0.775
O41
14
25.05
4.874
Total
251
2
107
108.28
0.015
18
15.47
0.414
10
15.78
2.116
20
15.47
1.327
155
3
60
66.37
0.611
8
9.48
0.231
11
9.67
0.183
16
9.48
4.482
95
Total
350
50
51
50
501
1
Chi-Sq = 15.407, DF = 6, P-Value = 0.017
MTB > print c6-c9
Data Display
Row
1
2
012
290
60
O22
42
8
O32
40
11
O42
34
16
36
252y0621s1 11/4/06
MTB > ChiSquare C6 C7 C8 C9
Chi-Square Test: 012, O22, O32, O42
Expected counts are printed below observed counts
Chi-Square contributions are printed below expected counts
012
290
283.63
0.143
O22
42
40.52
0.054
O32
40
41.33
0.043
O42
34
40.52
1.049
Total
406
2
60
66.37
0.611
8
9.48
0.231
11
9.67
0.183
16
9.48
4.482
95
Total
350
50
51
50
501
1
Chi-Sq = 6.796, DF = 3, P-Value = 0.079
MTB > print c11-c14
Data Display
Row
1
2
P1
0.171429
0.828571
P2
0.16
0.84
P3
0.215686
0.784314
P4
0.32
0.68
MTB > let c1(1) = c1(1) + 1
MTB > let c6(1) = c6(1) + 1
MTB > end
37
252y0621s1 11/4/06
Takehome Problem 3 Version 4
MTB
MTB
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#252062-t3 #Does last take-home problem
Name c1 'O11'
Name c2 'O21'
name c3 'O31'
name c4 'O41'
name c6 '012'
name C7 'O22'
name c8 'O32'
name c9 'O42'
name c11 'P1'
name c12 'P2'
name c13 'P3'
name c14 'P4'
let c11(1) = c6(2)/(c6(1)+c6(2))
let c12(1) = c7(2)/(c7(1)+c7(2))
let c13(1) = c8(2)/(c8(1)+c8(2))
let c14(1) = c9(2)/(c9(1)+c9(2))
let c11(2) = 1 - c11(1)
let c12(2) = 1 - c12(1)
let c13(2) = 1 - c13(1)
let c14(2) = 1 - c14(1)
MTB > Print c1-c4
Data Display
Row
1
2
3
O11
184
107
60
O21
24
18
8
O31
30
10
11
O41
14
20
16
MTB > ChiSquare C1 C2 C3 C4
Chi-Square Test: O11, O21, O31, O41
Expected counts are printed below observed counts
Chi-Square contributions are printed below expected counts
O11
184
176.20
0.345
O21
24
25.10
0.048
O31
30
25.60
0.756
O41
14
25.10
4.908
Total
252
2
107
108.38
0.017
18
15.44
0.425
10
15.75
2.097
20
15.44
1.348
155
3
60
66.42
0.621
8
9.46
0.226
11
9.65
0.188
16
9.46
4.517
95
Total
351
50
51
50
502
1
Chi-Sq = 15.499, DF = 6, P-Value = 0.017
MTB > print c6-c9
Data Display
Row
1
2
012
291
60
O22
42
8
O32
40
11
O42
34
16
38
252y0621s1 11/4/06
MTB > ChiSquare C6 C7 C8 C9
Chi-Square Test: 012, O22, O32, O42
Expected counts are printed below observed counts
Chi-Square contributions are printed below expected counts
012
291
284.58
0.145
O22
42
40.54
0.053
O32
40
41.35
0.044
O42
34
40.54
1.054
Total
407
2
60
66.42
0.621
8
9.46
0.226
11
9.65
0.188
16
9.46
4.517
95
Total
351
50
51
50
502
1
Chi-Sq = 6.849, DF = 3, P-Value = 0.077
MTB > print c11-c14
Data Display
Row
1
2
P1
0.170940
0.829060
P2
0.16
0.84
P3
0.215686
0.784314
P4
0.32
0.68
MTB > let c1(1) = c1(1) + 1
MTB > let c6(1) = c6(1) + 1
MTB > end
39
252y0621s1 11/4/06
Takehome Problem 3 Version 5
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#252062-t3 #Does last take-home problem
Name c1 'O11'
Name c2 'O21'
name c3 'O31'
name c4 'O41'
name c6 '012'
name C7 'O22'
name c8 'O32'
name c9 'O42'
name c11 'P1'
name c12 'P2'
name c13 'P3'
name c14 'P4'
let c11(1) = c6(2)/(c6(1)+c6(2))
let c12(1) = c7(2)/(c7(1)+c7(2))
let c13(1) = c8(2)/(c8(1)+c8(2))
let c14(1) = c9(2)/(c9(1)+c9(2))
let c11(2) = 1 - c11(1)
let c12(2) = 1 - c12(1)
let c13(2) = 1 - c13(1)
let c14(2) = 1 - c14(1)
MTB > Print c1-c4
Data Display
Row
1
2
3
O11
185
107
60
O21
24
18
8
O31
30
10
11
O41
14
20
16
MTB > ChiSquare C1 C2 C3 C4
Chi-Square Test: O11, O21, O31, O41
Expected counts are printed below observed counts
Chi-Square contributions are printed below expected counts
O11
185
177.05
0.357
O21
24
25.15
0.053
O31
30
25.65
0.737
O41
14
25.15
4.943
Total
253
2
107
108.47
0.020
18
15.41
0.436
10
15.72
2.079
20
15.41
1.369
155
3
60
66.48
0.632
8
9.44
0.221
11
9.63
0.194
16
9.44
4.552
95
Total
352
50
51
50
503
1
Chi-Sq = 15.592, DF = 6, P-Value = 0.016
MTB > print c6-c9
Data Display
Row
1
2
012
292
60
O22
42
8
O32
40
11
O42
34
16
40
252y0621s1 11/4/06
MTB > ChiSquare C6 C7 C8 C9
Chi-Square Test: 012, O22, O32, O42
Expected counts are printed below observed counts
Chi-Square contributions are printed below expected counts
012
292
285.52
0.147
O22
42
40.56
0.051
O32
40
41.37
0.045
O42
34
40.56
1.060
Total
408
2
60
66.48
0.632
8
9.44
0.221
11
9.63
0.194
16
9.44
4.552
95
Total
352
50
51
50
503
1
Chi-Sq = 6.903, DF = 3, P-Value = 0.075
MTB > print c11-c14
Data Display
Row
1
2
P1
0.170455
0.829545
P2
0.16
0.84
P3
0.215686
0.784314
P4
0.32
0.68
MTB > let c1(1) = c1(1) + 1
MTB > let c6(1) = c6(1) + 1
MTB > end
41
252y0621s1 11/4/06
Takehome Problem 3 Version 6
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#252062-t3 #Does last take-home problem
Name c1 'O11'
Name c2 'O21'
name c3 'O31'
name c4 'O41'
name c6 '012'
name C7 'O22'
name c8 'O32'
name c9 'O42'
name c11 'P1'
name c12 'P2'
name c13 'P3'
name c14 'P4'
let c11(1) = c6(2)/(c6(1)+c6(2))
let c12(1) = c7(2)/(c7(1)+c7(2))
let c13(1) = c8(2)/(c8(1)+c8(2))
let c14(1) = c9(2)/(c9(1)+c9(2))
let c11(2) = 1 - c11(1)
let c12(2) = 1 - c12(1)
let c13(2) = 1 - c13(1)
let c14(2) = 1 - c14(1)
MTB > Print c1-c4
Data Display
Row
1
2
3
O11
186
107
60
O21
24
18
8
O31
30
10
11
O41
14
20
16
MTB > ChiSquare C1 C2 C3 C4
Chi-Square Test: O11, O21, O31, O41
Expected counts are printed below observed counts
Chi-Square contributions are printed below expected counts
O11
186
177.90
0.369
O21
24
25.20
0.057
O31
30
25.70
0.719
O41
14
25.20
4.977
Total
254
2
107
108.56
0.022
18
15.38
0.447
10
15.68
2.060
20
15.38
1.390
155
3
60
66.54
0.642
8
9.42
0.215
11
9.61
0.200
16
9.42
4.588
95
Total
353
50
51
50
504
1
Chi-Sq = 15.686, DF = 6, P-Value = 0.016
MTB > print c6-c9
Data Display
Row
1
2
012
293
60
O22
42
8
O32
40
11
O42
34
16
42
252y0621s1 11/4/06
MTB > ChiSquare C6 C7 C8 C9
Chi-Square Test: 012, O22, O32, O42
Expected counts are printed below observed counts
Chi-Square contributions are printed below expected counts
012
293
286.46
0.149
O22
42
40.58
0.050
O32
40
41.39
0.046
O42
34
40.58
1.066
Total
409
2
60
66.54
0.642
8
9.42
0.215
11
9.61
0.200
16
9.42
4.588
95
Total
353
50
51
50
504
1
Chi-Sq = 6.957, DF = 3, P-Value = 0.073
MTB > print c11-c14
Data Display
Row
1
2
P1
0.169972
0.830028
P2
0.16
0.84
P3
0.215686
0.784314
P4
0.32
0.68
MTB > let c1(1) = c1(1) + 1
MTB > let c6(1) = c6(1) + 1
MTB > end
43
252y0621s1 11/4/06
Takehome Problem 3 Version 7
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#252062-t3 #Does last take-home problem
Name c1 'O11'
Name c2 'O21'
name c3 'O31'
name c4 'O41'
name c6 '012'
name C7 'O22'
name c8 'O32'
name c9 'O42'
name c11 'P1'
name c12 'P2'
name c13 'P3'
name c14 'P4'
let c11(1) = c6(2)/(c6(1)+c6(2))
let c12(1) = c7(2)/(c7(1)+c7(2))
let c13(1) = c8(2)/(c8(1)+c8(2))
let c14(1) = c9(2)/(c9(1)+c9(2))
let c11(2) = 1 - c11(1)
let c12(2) = 1 - c12(1)
let c13(2) = 1 - c13(1)
let c14(2) = 1 - c14(1)
MTB > Print c1-c4
Data Display
Row
1
2
3
O11
187
107
60
O21
24
18
8
O31
30
10
11
O41
14
20
16
MTB > ChiSquare C1 C2 C3 C4
Chi-Square Test: O11, O21, O31, O41
Expected counts are printed below observed counts
Chi-Square contributions are printed below expected counts
O11
187
178.75
0.381
O21
24
25.25
0.062
O31
30
25.75
0.701
O41
14
25.25
5.011
Total
255
2
107
108.65
0.025
18
15.35
0.459
10
15.65
2.042
20
15.35
1.411
155
3
60
66.59
0.653
8
9.41
0.210
11
9.59
0.206
16
9.41
4.623
95
Total
354
50
51
50
505
1
Chi-Sq = 15.782, DF = 6, P-Value = 0.015
MTB > print c6-c9
Data Display
Row
1
2
012
294
60
O22
42
8
O32
40
11
O42
34
16
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252y0621s1 11/4/06
MTB > ChiSquare C6 C7 C8 C9
Chi-Square Test: 012, O22, O32, O42
Expected counts are printed below observed counts
Chi-Square contributions are printed below expected counts
012
294
287.41
0.151
O22
42
40.59
0.049
O32
40
41.41
0.048
O42
34
40.59
1.071
Total
410
2
60
66.59
0.653
8
9.41
0.210
11
9.59
0.206
16
9.41
4.623
95
Total
354
50
51
50
505
1
Chi-Sq = 7.011, DF = 3, P-Value = 0.072
MTB > print c11-c14
Data Display
Row
1
2
P1
0.169492
0.830508
P2
0.16
0.84
P3
0.215686
0.784314
P4
0.32
0.68
MTB > let c1(1) = c1(1) + 1
MTB > let c6(1) = c6(1) + 1
MTB > end
45
252y0621s1 11/4/06
Takehome Problem 3 Version 8
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#252062-t3 #Does last take-home problem
Name c1 'O11'
Name c2 'O21'
name c3 'O31'
name c4 'O41'
name c6 '012'
name C7 'O22'
name c8 'O32'
name c9 'O42'
name c11 'P1'
name c12 'P2'
name c13 'P3'
name c14 'P4'
let c11(1) = c6(2)/(c6(1)+c6(2))
let c12(1) = c7(2)/(c7(1)+c7(2))
let c13(1) = c8(2)/(c8(1)+c8(2))
let c14(1) = c9(2)/(c9(1)+c9(2))
let c11(2) = 1 - c11(1)
let c12(2) = 1 - c12(1)
let c13(2) = 1 - c13(1)
let c14(2) = 1 - c14(1)
MTB > Print c1-c4
Data Display
Row
1
2
3
O11
188
107
60
O21
24
18
8
O31
30
10
11
O41
14
20
16
MTB > ChiSquare C1 C2 C3 C4
Chi-Square Test: O11, O21, O31, O41
Expected counts are printed below observed counts
Chi-Square contributions are printed below expected counts
O11
188
179.60
0.392
O21
24
25.30
0.066
O31
30
25.80
0.683
O41
14
25.30
5.045
Total
256
2
107
108.75
0.028
18
15.32
0.470
10
15.62
2.024
20
15.32
1.432
155
3
60
66.65
0.664
8
9.39
0.205
11
9.58
0.212
16
9.39
4.658
95
Total
355
50
51
50
506
1
Chi-Sq = 15.879, DF = 6, P-Value = 0.014
MTB > print c6-c9
Data Display
Row
1
2
012
295
60
O22
42
8
O32
40
11
O42
34
16
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252y0621s1 11/4/06
MTB > ChiSquare C6 C7 C8 C9
Chi-Square Test: 012, O22, O32, O42
Expected counts are printed below observed counts
Chi-Square contributions are printed below expected counts
012
295
288.35
0.153
O22
42
40.61
0.047
O32
40
41.42
0.049
O42
34
40.61
1.077
Total
411
2
60
66.65
0.664
8
9.39
0.205
11
9.58
0.212
16
9.39
4.658
95
Total
355
50
51
50
506
1
Chi-Sq = 7.065, DF = 3, P-Value = 0.070
MTB > print c11-c14
Data Display
Row
1
2
P1
0.169014
0.830986
P2
0.16
0.84
P3
0.215686
0.784314
P4
0.32
0.68
MTB > let c1(1) = c1(1) + 1
MTB > let c6(1) = c6(1) + 1
MTB > end
47
252y0621s1 11/4/06
Takehome Problem 3 Version 9
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#252062-t3 #Does last take-home problem
Name c1 'O11'
Name c2 'O21'
name c3 'O31'
name c4 'O41'
name c6 '012'
name C7 'O22'
name c8 'O32'
name c9 'O42'
name c11 'P1'
name c12 'P2'
name c13 'P3'
name c14 'P4'
let c11(1) = c6(2)/(c6(1)+c6(2))
let c12(1) = c7(2)/(c7(1)+c7(2))
let c13(1) = c8(2)/(c8(1)+c8(2))
let c14(1) = c9(2)/(c9(1)+c9(2))
let c11(2) = 1 - c11(1)
let c12(2) = 1 - c12(1)
let c13(2) = 1 - c13(1)
let c14(2) = 1 - c14(1)
MTB > Print c1-c4
Data Display
Row
1
2
3
O11
189
107
60
O21
24
18
8
O31
30
10
11
O41
14
20
16
MTB > ChiSquare C1 C2 C3 C4
Chi-Square Test: O11, O21, O31, O41
Expected counts are printed below observed counts
Chi-Square contributions are printed below expected counts
O11
189
180.46
0.404
O21
24
25.35
0.071
O31
30
25.85
0.666
O41
14
25.35
5.078
Total
257
2
107
108.84
0.031
18
15.29
0.482
10
15.59
2.005
20
15.29
1.454
155
3
60
66.71
0.674
8
9.37
0.200
11
9.56
0.218
16
9.37
4.693
95
Total
356
50
51
50
507
1
Chi-Sq = 15.977, DF = 6, P-Value = 0.014
MTB > print c6-c9
Data Display
Row
1
2
012
296
60
O22
42
8
O32
40
11
O42
34
16
48
252y0621s1 11/4/06
MTB > ChiSquare C6 C7 C8 C9
Chi-Square Test: 012, O22, O32, O42
Expected counts are printed below observed counts
Chi-Square contributions are printed below expected counts
012
296
289.29
0.155
O22
42
40.63
0.046
O32
40
41.44
0.050
O42
34
40.63
1.082
Total
412
2
60
66.71
0.674
8
9.37
0.200
11
9.56
0.218
16
9.37
4.693
95
Total
356
50
51
50
507
1
Chi-Sq = 7.120, DF = 3, P-Value = 0.068
MTB > print c11-c14
Data Display
Row
1
2
MTB
MTB
MTB
MTB
P1
0.168539
0.831461
P2
0.16
0.84
P3
0.215686
0.784314
P4
0.32
0.68
> let c1(1) = c1(1) + 1
> let c6(1) = c6(1) + 1
> end
>
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