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 shows the number of strikes each player threw before and after the training.
Before: 28, 29, 30, 32, 32, 32, 32, 32, 32, 33, 33, 33, 34, 34, 34, 35, 36, 36, 37, 37
After: 35, 36, 32, 28, 30, 31, 32, 34, 35, 36, 33, 35, 32, 33, 33, 34, 37, 33, 35, 32
A) Is there any evidence that after training, players can throw strikes more than 60% of the time? (Note that this is a one sample test and that the data are in counts, not percent, so you should not use .60, but rather 60% of 50=30 in your test calculations)
B) Is there evidence that the training is effective in improving a player's ability to throw strikes? (Note that this is now a paired sample test)