An article in the Journal of Sports Science presents the results of an investiga
ID: 3134362 • Letter: A
Question
An article in the Journal of Sports Science presents the results of an investigation of the hemoglobin level of Canadian Olympic ice hockey players. The data reported are as follows (in g/dl):
15.3
16.0
14.4
16.2
16.2
14.9
15.7
15.3
14.6
15.7
16.0
15.0
15.7
16.2
14.7
14.8
14.6
15.6
14.5
15.2
(a) Given the above probability plot of the data, what is a logical assumption about the underlying distribution of the data?
(b) Explain why this check of the distribution underlying the sample data is important if we want to construct a CI on the mean.
(c) Based on these sample data, a 95% CI for the mean is [15.04, 15.62]. Is it reasonable to infer that the true mean could be 14.5? Explain your answer.
(d) Explain why this check of the distribution underlying the sample data is important if we want to construct a CI on the variance.
(e) Based on these sample data, a 95% CI for variance is [0.22, 0.82]. Is it reasonable to infer that the true variance could be 0.35? Explain your answer.
(f) Is it reasonable to use these Cis to draw an inference about the mean and variance of hemoglobin levels
i. Of Canadian doctors? Explain your answer.
ii. Of Canadian children ages 6-12? Explain your answer.
An article in the Journal of Sports Science presents the results of an investigation of the hemoglobin level of Canadian Olympic ice hockey players. The data reported are as follows (in g/dl):
15.3
16.0
14.4
16.2
16.2
14.9
15.7
15.3
14.6
15.7
16.0
15.0
15.7
16.2
14.7
14.8
14.6
15.6
14.5
15.2
(a) Given the above probability plot of the data, what is a logical assumption about the underlying distribution of the data?
(b) Explain why this check of the distribution underlying the sample data is important if we want to construct a CI on the mean.
(c) Based on these sample data, a 95% CI for the mean is [15.04, 15.62]. Is it reasonable to infer that the true mean could be 14.5? Explain your answer.
(d) Explain why this check of the distribution underlying the sample data is important if we want to construct a CI on the variance.
(e) Based on these sample data, a 95% CI for variance is [0.22, 0.82]. Is it reasonable to infer that the true variance could be 0.35? Explain your answer.
(f) Is it reasonable to use these Cis to draw an inference about the mean and variance of hemoglobin levels
i. Of Canadian doctors? Explain your answer.
ii. Of Canadian children ages 6-12? Explain your answer.
Explanation / Answer
a) Given, th eprobability plot, the logical assumption of the sample data is that it follows normal distribution.
b) Normal probability plot finds the values one expect in a sample of 20 as the given one drawn from standard dnormal distribution. If plot deviates vertically from diagonal then it implies values are trending away from center suggesting that distribution is skewed. So this check is important.
c) One can be 95% confident that the true population mean will be within 15.04 and 15.62, therefore, it cannot be 14.5
d) One can be 95% confident that the tru epopulation variance will be within 0.22 and 0.82, and therefore, a variance of 0.32 is reasonable.
f) This is not suitable to draw inference about Canadian doctors or of Canadian children aged 6-12 from the data corresponding to haemoglobin level of Canadian ice-hockey players. As haemoglobin level of these players are assumed to be different from general people due to the difference in temperature.
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