Willis has noticed that when time has been one of the variables analyzed by a scatterplot he has looked at, it has always been the independent variable. He has hypothesized that time can never be a dependent variable. Does the scatterplot below confirm or invalidate Willis’s hypothesis?

Question

A graph titled Distance Traveled versus Time has Distance Traveled (miles) on the x-axis and Time (hours) on the y-axis. Plots pointed are (50, 1.2), (95, 2.3), (150, 2.6), (185, 3.8), (248, 4.4).
It confirms his hypothesis because the scatterplot must have been created incorrectly.
It confirms his hypothesis because time is the independent variable and distance traveled is the dependent variable.
It invalidates his hypothesis because it is possible for the time a trip takes to depend on the distance that is traveled during the trip.
It invalidates his hypothesis because it is possible for the distance that is traveled during a trip to depend on the time that is spent traveling.

Answer 1

The correct answer is:

It invalidates his hypothesis because it is possible for the distance that is traveled during a trip to depend on the time that is spent traveling.

In this scatterplot, time is the dependent variable, meaning that the distance traveled can vary based on the time spent traveling. While the scenario described shows distance versus time, various contexts could exist where time might depend on distance (such as when traveling at a constant speed, for instance). Therefore, Willis’s hypothesis is invalidated by the possibility that time can be treated as a dependent variable in certain situations.