An article that appeared in the British Medical Journal (2010) presented the results of a study conducted by researcher Jeremy Groves, whose objective was to determine whether the type of frame of his bicycle could affect his travel time to work. On each of 56 days (from mid-January to mid-July 2010), Dr. Groves tossed a coin to decide whether he would ride the 27 miles to work on his carbon frame bicycle that was light in weight, weighing 20.9 lb, or on his steel frame bicycle that was heavier, weighing 29.75 lb. He then recorded the commute time for each trip and the results (in minutes) are in the file BikeTimes. We want to determine if one of the bikes takes less time, on average, than the other.

a. What are the experimental units in this study and how many are there? 

b. What are the variables, what types are they (quantitative or categorical), and what are their roles (explanatory or response)? 

c. State the hypotheses to test this either in words or using appropriate symbols. 

d. What are the mean bike times for the two groups? Which type of bike is faster, on average? 

e. What is the p-value? 

f. Is there strong evidence that one of the bikes takes less time, on average, than the other? Explain.