16. The following resting data were collected from three different sports teams (hockey, rugby and football). Ignoring the sport played, run a Kolmogorov–Smirnov test on the age variable. What is the correct expression for the result?
ID 
Sport 
Age (y) 
Body mass (kg) 
Stature (m) 
Resting heart rate (bpm) 
Resting systolic blood pressure (mmHg) 
Resting diastolic blood pressure (mmHg) 
Resting mean arterial pressure (mmHg) 
1 
Hockey 
18 
79 
1.83 
65 
121 
79 
93 
2 
Hockey 
20 
79.9 
1.78 
50 
127 
81 
96 
3 
Hockey 
25 
75.8 
1.83 
53 
120 
62 
81 
4 
Hockey 
17 
63.6 
1.7 
74 
115 
75 
88 
5 
Hockey 
22 
57.4 
1.64 
68 
116 
68 
84 
6 
Hockey 
22 
60 
1.65 
64 
100 
30 
53 
7 
Hockey 
21 
81.2 
1.79 
65 
126 
80 
95 
8 
Hockey 
19 
84.5 
1.93 
64 
120 
70 
87 
9 
Rugby 
19 
71.1 
1.77 
79 
120 
80 
93 
10 
Rugby 
26 
72.8 
1.79 
82 
134 
76 
95 
11 
Rugby 
29 
75.1 
1.78 
55 
130 
90 
103 
12 
Rugby 
21 
69.4 
1.74 
60 
140 
71 
94 
13 
Rugby 
19 
68.8 
1.8 
76 
122 
78 
93 
14 
Rugby 
19 
63.8 
1.6 
61 
119 
74 
89 
15 
Rugby 
19 
87 
1.87 
60 
130 
80 
97 
16 
Football 
24 
74.2 
1.77 
63 
120 
64 
83 
17 
Football 
26 
80.9 
1.82 
65 
110 
79 
89 
18 
Football 
27 
66.5 
1.75 
63 
120 
50 
73 
19 
Football 
19 
83 
1.81 
49 
120 
80 
93 
20 
Football 
21 
89.5 
1.78 
50 
117 
80 
92 
21 
Football 
19 
74.2 
1.77 
72 
114 
78 
90 
22 
Football 
21 
66.6 
175 
83 
122 
82 
95 
a. 
D(22) = .197, p = .026 

b. 
D(22) = .026, p = .197 

c. 
D(22) = .086, p > .2 

d. 
D(22) = .2, p > .086 
17. Why does a Shapiro–Wilk test sometimes conclude that the data are not normally distributed (i.e. significant) when a Kolmogorov–Smirnov test is nonsignificant?
a. 
The Shapiro–Wilk test is more powerful. 

b. 
The Shapiro–Wilk test is less powerful. 

c. 
The Shapiro–Wilk test does not work well when there are a large number of cases. 

d. 
The Shapiro–Wilk test is a more conservative test. 
18. Using the data from the table in Q16, what assumption can be made regarding the distribution of the age data?
a. 
They are not normally distributed. 

b. 
They are normally distributed. 

c. 
It is unclear whether they are normally distributed or not. 

d. 
A Shapiro–Wilk test should be run to confirm the result. 
20.
Using the data in the table in Q16, split the data according to the sport. Run a Kolmogorov–Smirnov test on the diastolic blood pressure data. Which group’s data cannot assume a normal distribution?
a. 
Football 

b. 
Hockey 

c. 
Rugby 

d. 
All three are normally distributed. 
ShapiroWilk test, using righttailed normal distribution
1. H_{0}
hypothesis
Since pvalue<α, H_{0} is rejected.
It is assumed that the data is not normally distributed.
In other words, the difference between the data sample and the
normal distribution is big enough to be statistically
significant.
2.
Pvalue
pvalue is 0.0213364, hence, the chance of type1
error (rejecting a correct H_{0}) is small:
0.02134(2.13%)
The smaller the pvalue, the more it supports H_{1}
3. The
statistics
W is 0.892743. It is not in the 95% critical value
accepted range: [0.9112: 1.0000]
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