6. 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 clock 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 original 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. To formulate the process as a hypothesis test, the null hypothesis is that the player hypothesis is that the player , and the alternative . The testing procedure then assumes that the player with a goal of determining whether there is enough evidence to infer that the player
6. 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 clock 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 original 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. To formulate the process as a hypothesis test, the null hypothesis is that the player hypothesis is that the player , and the alternative . The testing procedure then assumes that the player with a goal of determining whether there is enough evidence to infer that the player
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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6. A sports analogy for hypothesis tests
V
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 clock 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 original 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.
To formulate the process as a hypothesis test, the null hypothesis is that the player
hypothesis is that the player
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Expert Solution
Step 1
There are two types of hypothesis -null and alternative; the null hypothesis is a statement about the population parameter while the alternative hypothesis contradicts the statement mentioned in the null hypothesis. The sign includes in the former hypothesis are while for later hypothesis the appropriate signs are .
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