Quiz
Questions 1-3 are based on the following quarterly data collected on the average nights foreign tourists spent in Washington DC area from 2011-2016 (quarterly data).
|
Time
|
Average Stay (nights)
|
|
Mar-11 1
|
41.7
|
|
Jun-11 2
|
24
|
|
Sep-11 3
|
32.3
|
|
Dec-11 4
|
37.3
|
|
Mar-12 5
|
46.2
|
|
Jun-12 6
|
29.3
|
|
Sep-12 7
|
36.5
|
|
Dec-12 8
|
43
|
|
Mar-13 9
|
48.9
|
|
Jun-13 10
|
31.2
|
|
Sep-13 11
|
37.7
|
|
Dec-13 12
|
40.4
|
|
Mar-14 13
|
51.2
|
|
Jun-14 14
|
31.9
|
|
Sep-14 15
|
41
|
|
Dec-14 16
|
43.8
|
|
Mar-15 17
|
55.6
|
|
Jun-15 18
|
33.9
|
|
Sep-15 19
|
42.1
|
|
Dec-15 20
|
45.6
|
|
Mar-16 21
|
59.8
|
|
Jun-16 22
|
35.2
|
|
Sep-16 23
|
44.3
|
|
Dec-16 24
|
47.9
|
1. Use Exponential Smoothing with w=0.6 to predict average stay (nights) by foreign tourists during four (4) quarters of 2017.
2. Assuming there is a trend in the data, use appropriate smoothing technique with coefficients w=0.6 and ν=0.2, to predict the average stay (nights) by foreign tourists during four (4) quarters of 2017.
3. Which of the above two models do you prefer? Why?,.. use MAD goodness of test in answering this question.
4. Which one the assumption (if any) is/are required for using Kruskal-Wallis test?
I. We assume that the samples drawn from the population are random.
II. We also assume that the cases of each group are independent.
III. The measurement scale for should be at least ordinal.
A. I, II but not III
B. I, III but not II
C. I, II and III
D. Kruskal-Wallis is a distribution free statistics and therefore no assumption is required.
Questions 5-6 are based on the following data. Suppose weights of an exotic plant (lbs) are different based on treatments (no treatment, fertilizer, irrigation, or fertilizer and irrigation). Each weight samples that determined by the treatments is independent and random. Weight samples are not normally distributed.
|
NO
|
Fert
|
Irrig
|
F&I
|
|
0.15
|
1.34
|
0.23
|
2.03
|
|
0.02
|
0.14
|
0.04
|
0.27
|
|
0.16
|
0.02
|
0.34
|
0.92
|
|
0.37
|
0.08
|
0.16
|
1.07
|
|
0.22
|
0.08
|
0.05
|
2.38
|
|
0.02
|
|
|
2.38
|
5. Test whether the weights of plants are different under the treatments.
6. What is your conclusion and why.
7-8. Six restaurant food critics were randomly assigned to all four restaurants (A, B, C, and D) and asked to rate them on the scale of 0-100 (100 being the best)
|
Rater
|
A
|
B
|
C
|
D
|
|
1
|
70
|
61
|
82
|
74
|
|
2
|
77
|
75
|
88
|
76
|
|
3
|
76
|
67
|
90
|
80
|
|
4
|
80
|
63
|
96
|
76
|
|
5
|
84
|
66
|
92
|
84
|
|
6
|
78
|
68
|
98
|
86
|
Are there any differences among the restaurant ratings? Please support your conclusion with objective facts/statistics.
9. Which of the following nonparametric tests can be used for a paired difference experiment?
a. The Wilcoxon Signed Ranks test.
b. The Sign test.
c. The Kruskal-Wallis test
d. Spearman's Rank Correlation test
10. The following table provides Math and English scores on 10 students. The relationship may not be linear. Use appropriate statistics to investigate the possible association between these scores
|
Exam
|
|
|
|
|
Scores
|
|
|
|
|
|
English
|
56
|
75
|
45
|
71
|
61
|
64
|
58
|
80
|
76
|
61
|
|
Maths
|
66
|
70
|
40
|
60
|
65
|
56
|
59
|
77
|
67
|
63
|