Do the Bengals score more points at Home?

During the 2014-15 NFL Season, the Cincinnati Bengals scored more points at home than on the road. Was this difference statistically significant?
The median points scored at home by the Bengals was 30 points. The median points scored in road games by the Bengals was 19.5 points.   To test this, we will use the test statistic median home points - median away points. What is the largest value of this test statistic? What is the smallest value of this test statistic? From looking at the box plots, does it appear that there is a statistical difference?

Conducting a Random Simulation

We can use a simulation to estimate a p-value. The physical details would be:
  • Write the all the points scored on index cards (16 total).
  • Shuffle these cards well
  • Divide the cards into two piles of eight cards each, one representing the home points scored, one representing the away points scored.
  • Compute the test statistic, and compare it to the test statistics of 10.5 points.
  • Repeat (in the simulation below, 100 times)
In the applet below, click on the NEW SIMULATION button to simulate 100 seasons.