Question

An article noted that it may be possible to accurately predict which way a penalty-shot kicker in soccer will direct his shot. \({ }^{27}\) 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?

Short answer

(a) Null hypothesis (H0): The proportion of kicks going right is not significantly different from 0.5. Alternative hypothesis (H1): The proportion of kicks going right is significantly different from 0.5. (b) With a p-value of 0.3184, we don't have enough evidence to reject H0. Goalkeepers should probably not prioritize learning to distinguish this movement. (c) With a p-value of 0.0006, we reject H0 in favor of H1, and goalkeepers should learn to distinguish this movement.

Step-by-step solution

Set Up Hypotheses

The null hypothesis (H0) in this case would state that the proportion of kicks that go right is not significantly different from 0.5, implying that the chance of the ball going either way is equal, not impacted by the player's body language. The alternative hypothesis (H1) would state that the proportion of kicks going right is significantly different from 0.5, indicating that the player's body language influences the direction of the kick.

Interpret P-value for the first body movement

The p-value is a probability that provides a measure of the evidence against the null hypothesis provided by the data. The smaller the p-value, the stronger the evidence against H0. A commonly used threshold to determine the significance is a p-value of 0.05. If p < 0.05, there's strong evidence against H0, and we reject it. If p > 0.05, we do not have enough evidence to reject the H0. With a p-value of 0.3184, which is greater than 0.05, there is insufficient evidence against the null hypothesis. Therefore, the body movement does not provide significant evidence about the direction of the kick.

Interpret P-value for the second body movement

With a p-value of 0.0006, which is much less than 0.05, there's significant evidence against the null hypothesis. Therefore, we reject H0 and accept H1: the proportion of kicks that go right, influenced by this particular body movement, is significantly different from 0.5. In this case, the goalkeeper should learn to distinguish this movement because it can help predict the direction of the kick.