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Running ultra-marathons may result in high levels of creatine kinase (CK) in the blood, which is associated with certain adverse health conditions. Hoffman et al. (2012) report a study in which they measured CK levels in the blood of some finishers of a 161 km race in 2010. Read the first three pages of the article:

Hoffman, M.D., Ingwerson, J.L., Rogers, I.R., Hew-Butler, T., Stuempfle, K.J. (2012): Increasing creatine kinase: Concentrations at the 161-km Western States Endurance Run. Wilderness and Environmental Medicine 23, 56-60.

Part (a) (WebWorkiR) What type of study is this?

A. A census
B. An experiment
C. An observational study

Part (b) (WebWorkiR) Consider the data underlying Table 1 in the article. The authors appear to apply ANOVA to the three groups. Why, if at all, is that approach incorrect?

A. The within-group variances are not the same.
B. The within-group means differ.
C. The data in the three groups are dependent.
D. There is no obvious reason why the approach would be incorrect.
E. There are too many missing values.

Part (c) (WebWorkiR) It appears that it was intended to measure both CK and sodium (Na) levels in the blood of all finishers of the race. Due to equipment failure, it was not possible to record the sodium levels of all finishers. The authors aim to investigate whether the characteristics of the runners differed across the different response groups, in particular with regards to finish time (in hours). It would be sensible to compare across three groups of finishers (CK, CK and sodium, no results). Suppose the data were as below:

$\begin{array}{c | c | c | c} & \text{CK only} & \text{CK and Na} & \text{No data} \\ \hline & & & \\ & & & \\ & \vdots & & \\ & & \vdots & \vdots \\ & & & \\ & & & \\ \hline \text{Sample Size} & 57 & 159 & 112 \\ \text{Mean} & & & \\ \text{S.D.} & & & \end{array}$

A. A stem-and-leaf plot
B. A bar chart
C. Three histograms plotted on the same axis
D. Side-by-side boxplots
E. Two scatter plots

Part(d) (WebWorkiR) The ANOVA table for the data is given below:

$\begin{array}{c | r r r r} \text{Source of variation} & \text{df} & \text{SS} & \text{MS} & \text{F}\\ \hline \text{Group} & 2 & & & \\ \text{Error} & 325 & & & \\ \hline \text{Total} & 327 & & & \end{array}$

Using R or otherwise, find the P-value of the test to 4 decimal places.

Part (e) (WebWorkiR) Do the data cast significant doubt on the hypothesis that the mean finishing times were equal in the three groups?

A. No
B. Yes

You can earn partial credit on this problem.