Question

In recent years, professional sports have incorporated the use of instant replay in order to dispute questionable calls by the referees. For example, in the National Basketball Association (NBA) a head coach is allowed to challenge the referees’ decision on whether a shot was made before time expired in the game. In order for the referees to reverse their original decision, the instant replay must exhibit clear evidence to the contrary.

Suppose the referees rule that the last shot of the game was made after the clock had expired. The coach of the team that made the shot believes the shot was made before time had expired, and the coach challenges the referees’ decision.

The referees will review all available evidence (video taken from different camera angles) and make a decision. If there is evidence beyond a reasonable doubt that their original call was incorrect, the basket will count. However, if there is no clear evidence to contradict the original call, the basket won’t count.

Notice the similarity between the decision to change a call and the decision to reject the null hypothesis in a hypothesis test. The process involves collecting convincing evidence that the original call or the null hypothesis is not true. The referee only rejects the call if the instant replay exhibits clear evidence to the contrary, just as a researcher only rejects the null hypothesis if the study results provide clear evidence to the contrary. In both cases, not changing the call and not rejecting the null hypothesis doesn’t mean that the original call or the null hypothesis was correct; it means that not enough evidence was provided to the contrary.

To formulate the process as a hypothesis test, the null hypothesis is that the player   , and the alternative hypothesis is that the player   . The testing procedure then assumes that the player   , with a goal of determining whether there is enough evidence to infer that the player   .

After the referees review video of all possible camera angles, according to the process of a hypothesis test, what two possible decisions can the referees make? (Hint: Remember that there are two possible decisions from a hypothesis test: you can either reject the null hypothesis or fail to reject the null hypothesis. Rejecting the null hypothesis means you have convincing evidence that the null hypothesis is false and the alternative hypothesis is true. Failing to reject the null means you do not have convincing evidence that the null hypothesis is false.) Check all that apply.

Conclude that the player made the shot after time expired

Conclude that they have convincing evidence to support the hypothesis that the player made the shot before time expired

Conclude that they have convincing evidence to support the hypothesis that the player made the shot after time expired

Conclude that they do not have convincing evidence to support the hypothesis that the player made the shot after time expired

Conclude that they do not have convincing evidence to support the hypothesis that the player made the shot before time expired

A Type I error occurs when you   a   null hypothesis. In this case, a Type I error corresponds to the referees concluding that they   evidence to support the hypothesis that the player   when the player actually   .

A Type II error occurs when you   a   null hypothesis. In this case, a Type II error corresponds to the referees concluding that they   evidence to support the hypothesis that the player   when the player actually   .

Answer 1