Multiple Choice Exercise
*** Choose one answer and click [Submit] button
10.1 What is NOT the reason to have a nonparametric test?
10.2 Which of the following nonparametric tests is for testing the location parameter of single population?
10.3 What is the sign test?
10.4 What is the transformation of data that is often used for nonparametric tests?
10.5 What is the test statistic used for the sign test?
10.6 Which of the following nonparametric tests is for testing the location parameters of two populations?
10.7 What is the test statistic used for testing two location parameters of two populations using a nonparametric test?
10.8 Which of the following nonparametric tests is for tesing the location parameters of multiple populations?
10.9 Which of the following nonparametric tests is appropriate for testing of the randomized block design method?
10.10 What is the theoretical basis for the statistic used for the Kruskal-Wallis test?
Practice Exercise
*** Answer the followings
10.1 A psychologist has selected 12 handicap workers randomly from production workers employed at various
factories in a large industrial complex and their work competency scores are examined as follows: The
psychologist wants to test whether the population average score is 45 or not. Assume the population distribution is symmetrical about the mean.
32, 52, 21, 39, 23, 55, 36, 27, 37, 41, 34, 51
1) Check whether a parametric test is possible.
2) Apply the sign test with the significance level of 5%.
3) Apply the Wilcoxon signed rank test with the significance level of 5%.
10.2 A tire production company wants to test whether a new manufacturing process can produce a more durable tire
than the existing process. The tire by a new process was tested to obtain the following data: (unit: 1000)
| Existing Process |
New Process |
62
76
61
90
74
74
75
63 |
73
53
61
65
60
53
70
63 |
1) Check whether a parametric test is possible.
2) Apply the Wilcoxon rank sum test whether the new process and the existing process have the same durability or not with the significance level of 5%.
10.3 A company wants to compare two methods of obtaining information about a new product. Among company
employees, 19 were randomly selected and divided into two groups. The first group learned about the new product
by the method A, and the second group learned by the method B. At the end of the experiment, the employees took a
test to measure their knowledge of the new product and their test scores are as follows: Can we conclude from
these data that the median values of the two groups are different? Test with the significance level of 0.05.
| Method A |
Method B |
50
59
60
71
80
78
72
77
73
75 |
52
54
58
78
65
61
60
72
60 |
10.4 10 men and 10 women working in the same profession were selected independently and their monthly
salaries were surveyed. Can you say that a man in this profession earns more than a woman. Test with the significance level of 0.05. (Unit: 10USD)
| Man |
Woman |
381
294
296
389
281
194
193
286
384
494 |
284
279
288
383
489
287
496
393
277
371 |
10.5 To find out the fuel mileage improvement effect of a new gasoline additive, 10 cars of the same state were
selected. The gas mileage was tested without gasoline additives and with additives running the same road at the
same speed and obtain the following data. Test whether the new gasoline additive is effective in improving the
fuel mileage with the significance level of 0.05. (gas mileage unit: km/liter)
| With additives |
Without additives |
11.7
13.8
11.2
7.7
8.2
16.3
14.2
19.4
13.9
15.5 |
10.3
12.9
12.5
9.5
11.2
14.6
15.9
18.5
12.0
15.1 |
10.6 In order to determine the efficacy of the new pain reliever, seven persons were tested with the aspirin
and new pain reliever. The experimental time of the two pain relievers were sufficiently spaced,
and the order of the medication experiment was randomly determined. The time (in minutes) until feeling pain relief
was measured as follows: Do the data indicate that the new pain reliever has faster pain relief than aspirin?
Test with the significance level of 0.05.
| id |
Aspirin |
New pain reliever |
1
2
3
4
5
6
7 |
15
20
12
20
17
14
17 |
7
14
13
11
10
16
11 |
10.7 A person was asked to taste 15 coffee samples to rank from 1 (hate first) to 15 (best). The 15 samples are
taken from each of the three types of coffee (A, B, C) and are tasted in random order. The following table shows
the ranking of preference by the coffee type. Test the null hypothesis that there is no difference in three types
of coffee preferences at the significance level of 0.05.
| Coffee A |
Coffee B |
Coffee C |
9
10
11
12
13 |
14
1
5
7
8 |
2
3
4
15
6 |
10.8 A bread maker wants to compare the four new mix of ingredients. 5 breads were made by each mixing ratio of
ingredients, a total of 20 breads, and a group of judges who did not know the difference in mixing ratio of
ingredients were given the following points. Test the null hypothesis that there is no difference in taste
according to the mixing ratio of ingredients at the significance level of 0.05.
| Method A |
Method B |
Method C |
Method D |
72
88
70
87
71 |
85
89
86
82
90 |
94
94
88
87
89 |
91
93
92
95
96 |