Advertisements for an instructional video claim that the techniques will improve the ability of Little League pitchers to throw strikes and that, after undergoing the training, players will be able to throw strikes on at least 60% of their pitches. To test this claim, we have 20 Little Leaguers throw 50 pitches each, and we record the number of strikes. After the players participate in the training program, we repeat the test. The table (on the next page) shows the number of strikes each player threw before and after the training.
a) Is there evidence that after training players can throw strikes more than 60% of the time?
b) Is there evidence that the training is effective in improving a player's ability to throw strikes?
c) Use a matched-pairs sign test to test the appropriate hypothesis. Do your conclusions change from those in part a?

Number of Strikes Number of Strikes (out of 50) Before After (out of 50) Before After 35 31 35 32 35 37 37 35