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.

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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