5. We are developing a simulation of the game of baseball. We want to measure how well our system simulates the margin of victory. In general, we like the margin of victory to be 1, 2, or 3 runs. A 4-run game isn't too bad, but games with margins of 5 or more runs are okay once in a while but aren't very interesting. So, after consulting baseball statistics to see what the margin of victory was in American and National League playoff games, we decide that we'd like the distribution of the margin of victory of games played by our system to be as shown on the "Ideal"

row in the following table. We develop two versions of the simulator and play 100 games with each system. The margins of victory from our simulations are shown on the lines for System 1 and System 2

Use the chi-square metric to analyze the two systems. At what level does each of them sustain the null hypothesis? Which one would you choose? Why? Is there a problem with using chi-square for this analysis? If so, what is it?

Transcribed Image Text:

Margin of victory 1 2 3 4 >=5 Ideal number of games 25 30 20 15 10 System 1 number of games 28 29 21 14 8 System 2 number of games 24 27 21 17 11