7. A sports analogy for hypothesis tests In recent years, professional sports ha

Question

7. 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 before the dlock had expired. The coach of the opposing team believes that time ran out before the shot was made, 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 won't count. However, if there is no clear evidence to contradict the orig call, the basket will remain counted. 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. , and the alternative To formulate the process as a hypothesis test, the null hypothesis is that the player 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 dedsions can th referees make? Check all that apply. (Hint: Remember that there are two possible decisions from a hypothesis test: you can either reject the null hypothesis or fail to reject the nuil 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.) 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 before time expired a Conclude that they do not have convincing evidence to support the hypothesis that the player made the shot after time expired conclude that the player made the shot before time expired null hypothesis. In this case, a Type I error corresponds to the referees concluding A Type I error occurs when you that they actually evidence to support the hypothesis that the player when the player A Type II error occurs when you that they actually null hypothesis. In this case, a Type I1 error corresponds to the referees concluding when the player evidence to support the hypothesis that the player

Explanation / Answer

1. The null hypothesis is that the player scored the last shot before the clock expired; i.e. the last shot counts.

Alternative hypothesis is that the player scored the last shot after the clock expired, i.e the time ran out before the last shot and the last shot doesn't count.

The testing procedure then assumes that the player scored the last shot before the clock expired, with the goal of determining whether there is enough evidence to infer that the player scored the last shot after the clock expired.

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

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

Type I error occurs when you reject a true null hypothesis.In this case, a Type I error corresponds to the referees concluding that they have convincing evidence to support the hypothesis that the player made the shot after the time expired, when the player actually scored the last shot before the clock expired.

Type II error occurs when you accept a false null hypothesis.In this case, a Type II error corresponds to the referees concluding that they do not  have convincing evidence to support the hypothesis that the player scored the shot after the time expired, when the player actually made the last shot after the clock expired.

Related Questions

Navigate

• Browse (All)
• Browse 7
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.