Question

16. The following resting data were collected from three different sports teams (hockey, rugby and football)....

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 non-significant?

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.

Homework Answers

Answer #1

Shapiro-Wilk test, using right-tailed normal distribution

1. H0 hypothesis
Since p-value<α, H0 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. P-value
p-value is 0.0213364, hence, the chance of type1 error (rejecting a correct H0) is small: 0.02134(2.13%)
The smaller the p-value, the more it supports H1

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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