Suppose that you play the game, again, with two other friends separately with the following results:
Friend D chose rock 200 times out of 400 games.
Friend E chose rock 20 times out of 40 games.

Suppose that for each friend you want to test whether the long-run proportion that the friend will pick rock is more than 1/3.
a. Even though both of the friends played rock the same proportion of times, one of the two friends’ data provide more evidence the null hypothesis is wrong. Which friend’s data do you think provides more evidence against the null hypothesis? Why?
b. Based on your answer to (a), which friend’s data yields a smaller p-value? Why?
c. Based on your answer to (a), which friend’s data yields a larger standardized statistic? Why?
d. Based on your answer to (c), which friend’s null distribution has a smaller standard deviation? Why?