A sports analogy for hypothesis tests
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.
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? Check all that apply.
Conclude that the player made the shot after time expired
Conclude that they do not have enough evidence to support the hypothesis that the player made the shot after time expired
Conclude that they do not have enough evidence to support the hypothesis that the player made the shot before time expired
Conclude that they have enough evidence to support the hypothesis that the player made the shot after time expired
Conclude that they have enough 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 _________ .