42.     Tour de France These data give the times in minutes for cyclists who competed in the 2010 Tour de France and raced in both time trial events. In a time trial, each cyclist individually rides a set course. The rider with the shortest time wins the event. The courses in the 2010 tour varied in length. The first time trial at the start of the month-long race was 8.9 kilometers long, and the second time trial near the end of the race was 52 kilometers long.

(a)   Would you expect the times to be associated?

(b)   Make a scatterplot of these data, with the first set of times along the x-axis. Do the variables appear to be associated? Describe the relationship, if any.

(c)    Find the correlation between these variables, if appropriate.

 

 

 

 

 

 

 

 

 

 

 

 

(a)  

Entered Errors 4,434 35 4,841 42 6,280 15 1,958 28 7,749 36 2,829 42 4,239 18 3,303 54 5,706 34 3,770 40 3,363 36 1,740 23 3,404 27 1,640 26 3,803 56 1,529 20

Make a scatterplot of these data. Which did you choose for the response and which

for the explanatory variable? Describe any patterns.

(b)   Find the correlation for these data.

(c)    Suppose we were to record the counts in the table in hundreds, so 4,434 became 44.34. How would the correlation change? Why?

(d)   Write a sentence or two that interprets the value of this correlation. Use language that would be understood by someone familiar with data entry rather than correlations.

(e)    One analyst concluded, “It is clear from this correlation that clerks who enter more values make more mistakes. Evidently they become tired as they enter more values.” Explain why this explanation is not an appropriate conclusion.