Question: Every summer, the touring company America-byBicycle conducts its Cross-Country Challenge, a seven week bicycle journey across the United States from San Francisco to Portsmouth, New Hampshire. At some point during the trip, the exhausted cyclists usually start to complain that the organizers are purposely planning for days with lots of hill and mountain climbing to coincide with longer distances. The staff who work on the tour counter that no relation exists between climbs and mileage and that the route is organized based on practicalities, such as the location of towns in which riders can stay. The organizers who planned the route (and who also own the company) say that they actually tried to reduce the mileage on the days with the worst climbs. Here are the approximate daily mileages and climbs (in vertical feet) as estimated from one rider's bicycle computer.
a. Construct a scatterplot of the cycling data, putting mileage on the x-axis. Be sure to label everything and include a title.
b. We haven't yet learned to calculate inferential statistics on these data, so we can't really know what's going on, but do you think that the amount of vertical climb is related to a day's mileage? If yes, explain the relation in your own words. If no, explain why you think there is no relation.
c. It turns out that inferential statistics do not support the existence of a relation between these variables and that the staff seem to be the most accurate in their appraisal. Why do you think the cyclists and organizers are wrong in opposite directions? What does this say about people's biases and the need for data?