ENGINEERING STATISTICS EQT 271 SEM 1 2013/2014
CHAPTER 5
TUTORIAL (NONPARAMETRIC STATISTICS)
1.
A six-sided die is rolled 30 times and the numbers 1 through 6 appear as shown in the following
frequency distribution. At the 0.10 significance level, can we conclude that the die is fair?
Outcome
1
2
3
4
5
6
2.
One article discusses the effects of exposure to beryllium on a cohort of workers. Workers
were categorized by their duration of exposure (in years) and by their disease status (chronic
beryllium disease, sensitive to beryllium or no disease). The results were as shown in the table.
Can you conclude that the proportions of workers in the various disease categories differ among
exposure level. Use   0.01
Diseased
Sensitive
Normal
3.
Frequency
3
6
2
3
9
7
Duration of exposure
<1
1 to < 5
10
8
9
19
70
136
>=5
23
11
206
To determine whether there really is a relationship between an employee’s performances in the
company’s training program and his or her ultimate success in the job, the company takes a
sample of 400 cases from its very extensive files and obtains the results shown in the following
table:
Success in job
Performance in training program
(empl
Below average
Average
Above Average
oyer`s
rating
)
Poor
23
60
29
Average
28
79
60
Very Good
9
49
63
Test that performance in training program and success in job are independent at   0.01 .
SYAFAWATI BINTI AB. SAAD
ENGINEERING STATISTICS EQT 271 SEM 1 2013/2014
4.
A study is conducted to determine whether type of painkiller administered to patients is
influencing the level of pain felt by patient and the following data set was obtained:
Painkiller
A
B
Level of Pain
No
20
10
A Little
30
35
Strong
10
15
Test whether the level of pain and the type of painkiller are independent at 1% significance
level.
5.
A total of 1000 PVC pipes are sampled and categorized with respect to both length and
diameter specification. The results are presented in the following table:
Length
Too Short
Meet Specification
Too long
Diameter
Too Thick
20
65
35
Meet Specification
115
550
145
Too Wide
15
45
10
Test at 1% significance level whether the length and diameter of the PVC pipes are
independent.
6.
A random sample of semiconductor devices is taken to observe the relationship between
classification and status for each device. The results as follows:
Status
Rejected
Non Rejected
Classification
Defective
80
40
Non Defective
20
60
Test the hypothesis that the status and classification are independent at 5% significance level.
7.
A study was conducted to determine whether the type of painkiller administered to patients is
influencing the level of pain felt by patient and the following data set was obtained:
Level of Pain
Painkiller
No
A Little
Strong
A
20
30
10
B
10
35
15
At 0.01 level of significance, test whether the type of painkiller is related with the level of pain.
SYAFAWATI BINTI AB. SAAD
ENGINEERING STATISTICS EQT 271 SEM 1 2013/2014
8.
9.
In problems (i)-(v), use the Wilcoxon Signed Rank Test to test the given hypothesis at 5%
significance level.
(i) Hypotheses H1 : Median of R(di )  0 with n  12 and T   16
(ii)
Hypotheses H1 : Median of R(di )  0 with n  15 and T   33
(iii)
Hypotheses H1 : Median of R(di )  0 with n  18 and T   121 and T   50
(iv)
Hypotheses H1 : Median of R(di )  0 with n  40 and T   300
(v)
Hypotheses H1 : Median of R(di )  0 with n  35 and T   210
Use the Wilcoxon Signed rank test to determine if the median of the population represented in
table below is different than 2.6. Use 0.05 significance level to test the claim.
2.1
1.8
2.3
2.9
1.8
2.6
3.1
2.2
2.5
2.4
10.
Eight students went on a diet in an attempt to lose weight, with the following results:
Name
Abu
Ali
Chen Rama Subra Lim
Tan
Amin
Weight Before (kg)
78
86
69
83
78
74
80
90
Weight After (kg)
66
87
64
80
73
65
75
87
Use the Wilcoxon signed-rank test to test whether the diet an effective men of losing weight at
significance level 0.05.
SYAFAWATI BINTI AB. SAAD
ENGINEERING STATISTICS EQT 271 SEM 1 2013/2014
11.
The following data gives the cholesterol levels for seven adults before and after they completed
a special dietary plan.
Before
210
180
195
220
231
199
224
After
193
186
186
223
220
183
233
Use the Wilcoxon signed-rank test at the 5% significance level to test whether the level of
cholesterol is the same before and after completing special dietary plan. Draw your conclusion.
12.
A semi conductor manufacturer claims that its production operators have increased their handinsert ability speed after attending a course. The following table gives the hand-insert ability
speed of 8 operators before and after they attend the course:
Before 74
After 87
65
62
78
83
81
100
55
68
61
59
80
105
65
66
Using Wilcoxon Signed Rank Test, test at 2.5% significance level that can we conclude
attending the course increases the hand-insert ability speed of operators?
13.
Based on data below, can you conclude at 5% significance level that population X is greater than
Y using Wilcoxon Sign Rank Test?
X
Y
5
8
3
4
7
6
9
9
8
6
14.
The achievement test scores for four different groups of students, each group taught by
different teaching technique. The objective of this experiment is to test the hypothesis of no
difference in the population distributions of achievement test scores versus the alternative that
they differ in location;that is , at least one of the distribution is shifted above the others.
Conduct the test using Kruskal Wallis H test with   0.05 .
1
65
87
73
79
81
69
2
75
69
83
81
72
79
90
3
59
78
67
62
83
76
4
94
89
80
88
SYAFAWATI BINTI AB. SAAD
ENGINEERING STATISTICS EQT 271 SEM 1 2013/2014
15.
The following table gives the ranked data for three samples. Perform the Kruskal-Wallis test
using 1% level of significance.
Sample I
3
1
10
7
9
6
16.
Sample II
14
11
16
15
12
At the end of the 15 students took the same arithmetic test. Their test scores are given in the
following table. At the 1% significance level (using Kruskal Wallis Test), can you reject the null
hypothesis that the median arithmetic test scores of all fourth-grade students taught by these
three methods are equal?
Method I
48
73
51
65
87
17.
Sample III
2
4.5
13
4.5
8
Method II
55
85
70
69
90
Method III
84
68
95
74
67
The following table gives the monthly premiums paid by the 20 drivers.
Company A
$65
73
54
43
70
Company B
$48
69
88
75
72
Company C
$57
61
89
77
69
Company D
$62
53
45
51
44
By using Kruskal Wallis test, can you reject the null hypothesis that the distributions of auto
insurance premiums paid per month by all drivers are the same for all four companies. Use 5%
significance level.
18.
Three nrands of 60-watt lightbulbs Brand A, B and a generic brand are tested for their lives.
The following table shows the lives (in hours) of these bulbs.
Brand A
975
1050
890
933
962
925
1007
855
Brand B
1001
1099
915
959
986
957
987
881
1025
Generic
899
789
824
1011
907
923
937
865
1024
Using Kruskal Wallis test with a significance level of 0.05, can you conclude that the
distributions of the lives of lightbulbs are the same for all three brands?
SYAFAWATI BINTI AB. SAAD
ENGINEERING STATISTICS EQT 271 SEM 1 2013/2014
19.
The following table gives the number of defective parts produced during each shift over a
period of five days.
First Shift
23
36
32
40
45
Second Shift
25
35
41
38
50
Third Shift
33
44
50
52
60
At 5 % significance level, can you conclude that the number of defective is the same for all
three shifts?(Kruskal Wallis)
20.
A researcher wanted to find out whether the population distributions of salaries of computer
programmers are identical in three cities, Boston, San Fransisco and Atlanta. Three different
samples one from each city produced the following data on the annual salaries (in thousand of
dollars) of computer programmers.
Boston
43
39
62
73
51
46
San Fransisco
54
33
58
38
43
55
34
Atlanta
57
68
60
39
28
49
57
44
Using 2.5% significance level, can you conclude that the population distributions of salaries for
computer programmers in these three cities are all identical? (Kruskal Wallis Test)
SYAFAWATI BINTI AB. SAAD