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 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 ___________________ , 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. (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.) - 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 - 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 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 __________________ .

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 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 _______________________________________ , 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. (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.)

- 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
- 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

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 ________________________________________ .

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 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 , 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. (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.)

- 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
- 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

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 .

Added by Lourdes C.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Madhur L

03/28/2023

Step 1

The null hypothesis (H0) is that the player made the shot after time expired (basket doesn't count). Show more…

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Professional sports have incorporated the use of instant replay to dispute questionable calls by the referees. For example, the National Basketball Association (NBA) allows coaches to challenge the referees' decision on whether a shot was made. If the referees reverse their original decision, the instant replay must exhibit clear evidence before time expires in the game. Before the clock had expired, the coach of the opposing team believes that the last shot of the game was out before the shot was made, and the coach challenges the referees' decision. Justifiable evidence, such as video taken from different camera angles, is used to make a decision. The referees will review all evidence, but 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 the null hypothesis, which assumes that the player did not make the shot. The referee only rejects the call or the null hypothesis when there is convincing evidence that the original call or null hypothesis is false. Just as researchers reject the null hypothesis when the study results provide clear evidence to the contrary, not changing the call and not rejecting the null hypothesis doesn't mean that the original call or null hypothesis is true. In both cases, it means that not enough evidence was provided to support the contrary. In the alternative formulation of the hypothesis test, the null hypothesis is that the player made the shot after time expired. The testing procedure involves reviewing video from all possible camera angles and determining whether there is convincing evidence to infer that the player made the shot before time expired. After the referees make their decision, you can either reject the null hypothesis, fail to reject the null hypothesis, or conclude that they have convincing evidence to support the hypothesis that the player made the shot before time expired.