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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI 600 034
M.Sc.DEGREE EXAMINATION STATISTICS
THIRDSEMESTER APRIL 2018
16PST3ES02- NON-PARAMETRIC METHODS
Date: 05-05-2018 Dept. No. Max. 100 Marks
Time: 09:00-12:00
SECTION A
Answer all the questions. (10 X 2 20)
1. When do we use Non parametric Methods?
2. Define Nominal and Ordinal data with an example.
3. Define Parameter ii) Statistic
4. In which situation we can use the run test for serial randomness?
5. State the situation for using Fishers test
6. State the applications of ordered alternative test for two way layout.
7. Name two non parametric tests will be used to compare more than two populations.
8. When do we use slope coefficient test?
9. State the applications of Hollander Test.
10. Write a short note on kernel density estimation.
SECTION- B
Answer any five questions. X 8 40)
11. Explain the test procedure for Kolmogorov-Smirnov test for two independent samples.
12. The following table gives the number of air craft accidents that occurred during the various
days of the week. Find whether the accidents are uniformly distributed over the week.
Day
Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
No.of Accidents
14
16
8
12
11
9
14
13. Explain in detail Wilcoxon signed rank test.
14. A survey is conducted to test the difference between two alternative methods of teaching. A
sample of 20 students is selected at random. Two groups of 10 students each of equal ability
are formed, and taught by different methods. A standardized test is given to both the groups
and the following marks are scored by the 10 students in each group.
Group A
40
45
48
46
52
58
72
85
67
73
Group B
42
68
45
64
85
78
87
62
84
90
Using U test, test the significance of difference between the performance of the two groups.
15. Do the J test with the following data
Control
40
35
38
43
44
41
Rough
38
40
47
44
40
42
Accurate
48
40
45
43
46
44
Use ordered alternative test and draw the inferences.
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16. Write the data layout, assumptions and test procedure of Kruskal wallis test.
17. To investigate the effects of a particular method of cloud seeding on the amount of rainfall.
In one experiment that took place in the snowy mountains, two areas served as target and
control, respectively, and during any one period a random process was used to determine
whether clouds over the target area should be seeded. The effect of seeding was measured by
the double ratio.
Years seeded(X)
1
2
3
4
5
Double Ratio(Y)
1.26
1.27
1.12
1.16
1.03
Test the hypothesis that the double ratio does not change with time.
18. Explain Gibbs sampling.
SECTION- C
Answer any two questions. X 20 40)
19. Explain the Binomial test in detail.
ii) Each person in a random sample of n 10 employees was asked about the daily time
wasted at work doing non-work activities(X), such as surfing the internet and emailing
friends. The resulting data in minutes are as follows:
108 112 117 130 111 131 113 113 105 128
Verify whether these data come from a normal distribution with mean 120 and
standard deviation 10.
20. Explain and write the test procedure for various two sample dispersion tests.
21. Consider twelve patients getting three different treatments Test whether the Treatment is
different using Fried Rank sums test and find which pairs of Treatments are different.
Patient
Treatment 1
Treatment 2
Treatment 3
1
209
88
109
2
412
388
142
3
315
451
155
4
389
325
121
5
210
126
75
6
136
118
49
7
178
227
101
8
228
98
49
9
240
205
142
10
113
88
45
11
178
194
55
12
321
349
121
22. Write the assumptions, procedure and interpretation for testing parallelism of two
regression lines.
ii) Write a short note on EM algorithm
Method of generating a random sample from a mixture
distribution