A recent article noted that it may be possible to accurately predict which way a penalty-shot kicker in soccer will direct his shot. The study finds that certain types of body language by a soccer player—called ‘‘tells”—can be accurately read to predict whether the ball will go left or right. For a given body movement leading up to the kick, the question is whether there is strong evidence that the proportion of kicks that go right is significantly different from one-half.

(a) What are the null and alternative hypotheses in this situation?

(b) If sample results for one type of body movement give a p-value of 0.3184, what is the conclusion of the test? Should a goalie learn to distinguish this movement?

(c) If sample results for a different type of body movement give a p-value of 0.0006, what is the conclusion of the test? Should a goalie learn to distinguish this movement?