Suppose that you play the game with three different friends separately with the following results:
Friend A chose scissors 100 times out of 400 games.
Friend B chose scissors 20 times out of 120 games.
Friend C chose scissors 65 times out of 300 games.
Suppose that for each friend you want to test whether the long-run proportion that the friend will pick scissors is less than 1/3.
a. Determine the appropriate standardized statistic for each friend’s results. (Hint: You will need to get the standard deviation of the simulated statistics from the null distribution produced by an applet.)
b. Based on the standardized statistics, which friend’s data provides the strongest evidence that the long-run proportion that the friend will choose scissors is less than 1/3? Which friend’s data provides the least strong evidence?