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

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7. A sports analogy for hypothesis tests Aa Aa 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 Football League (NFL) a head coach is allowed to challenge the referees' decision twice per 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 a pass was caught out of bounds. The head coach of the team that threw the ball believes the player completely caught the ball before stepping out of bounds, 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 play will be called a complete pass. However, if there is no clear evidence to contradict the original call, the play will remain ruled as an incomplete pass. 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 caught the ball in bounds caught the ball out of bounds

Explanation / Answer

The null hypothesis is that the player caught the ball out of bounds as that is what is decided by the referees and they shall reject the null only if there is sufficient evidence on the contrary. So, alterbate hypothesis is that the player caught the ball in bounds

In hypothesis take two decisions : we do not reject the null or reject the null. So, either we conclude that there is evidence that the player did not catch the ball out of bounds or we conclude that there is not sufficient evidence that the player did not catch the ball out of bounds

Type I error is when we reject a true null hypothesis. SO the player actually caught the ball oit of bounds but referees err that it was caught in bounds

Type II error is when we accept a false hypothesis. SO the player actually caught the ball in bounds but we conclude that it was caught out of bounds

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