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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 1. (made the shot before time expired OR made the shot after the time expired), and the alternative hypothesis is that the player 2. (made the shot before time expired OR made the shot after the time expired). The testing procedure then assumes that the player 3. (made the shot before time expired OR made the shot after the time expired) , with a goal of determining whether there is enough evidence to infer that the player 4.(made the shot before time expired OR made the shot after the time expired) . 5. 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? (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.) Check all that apply. A. Conclude that they have convincing evidence to support the hypothesis that the player made the shot before time expired B. Conclude that they have convincing evidence to support the hypothesis that the player made the shot after time expired C. Conclude that they do not have convincing evidence to support the hypothesis that the player made the shot before time expired D. Conclude that the player made the shot before time expired E. Conclude that they do not have convincing evidence to support the hypothesis that the player made the shot after time expired A Type I error occurs when you 6. (reject OR do not reject) a 7. (True OR False) null hypothesis. In this case, a Type I error corresponds to the referees concluding that they 8.(have convincing OR do not have convincing) evidence to support the hypothesis that the player 9. (made the shot before time expired OR made the shot after the time expired) when the player actually 10. (made the shot before time expired OR made the shot after the time expired) . A Type II error occurs when you 11. (reject OR do not reject) a 12. (True OR False) null hypothesis. In this case, a Type II error corresponds to the referees concluding that they 13. (have convincing OR do not have convincing) evidence to support the hypothesis that the player 14. (made the shot before time expired OR made the shot after the time expired) when the player actually 15. (made the shot before time expired OR made the shot after the time expired) . Provide a correct and error-free solution. Ensure the method is correct, there must be no calculation errors, and the solution is complete and well-framed properly and Don't give direct answers; it must be clear and properly framed and aligned. Avoid using personal pronouns like 'we', 'you', and 'I' in the answer. Give answer as a teacher that you are giving answer to a student and making them understand properly. Don't use Python, please. The solutions will be evaluated based on six key parameters: Relevancy , ensuring closely matches with the question; Completeness , including like calculations, diagrams, procedural steps, & explanatory statements in the solution.; Accuracy, ensuring correctness of concepts and methods; Clarity , assessing readability and simplicity of language; Structure , focusing on organization and presentation; and Voice , determining the response feels natural and human-like rather than robotic. Give a two-line best explanation or interpretation where there is a need for it. Give overall short final answer in last. The complete solution is lacking; please complete the whole answer till the end. Please adhere and strictly follow all these guidelines anyhow. Thank you.) dont use phython

Question:

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 1. (made the shot before time expired OR made the shot after the time expired), and the alternative hypothesis is that the player 2. (made the shot before time expired OR made the shot after the time expired). The testing procedure then assumes that the player 3. (made the shot before time expired OR made the shot after the time expired) , with a goal of determining whether there is enough evidence to infer that the player 4.(made the shot before time expired OR made the shot after the time expired) . 5. 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? (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.) Check all that apply. A. Conclude that they have convincing evidence to support the hypothesis that the player made the shot before time expired B. Conclude that they have convincing evidence to support the hypothesis that the player made the shot after time expired C. Conclude that they do not have convincing evidence to support the hypothesis that the player made the shot before time expired D. Conclude that the player made the shot before time expired E. Conclude that they do not have convincing evidence to support the hypothesis that the player made the shot after time expired A Type I error occurs when you 6. (reject OR do not reject) a 7. (True OR False) null hypothesis. In this case, a Type I error corresponds to the referees concluding that they 8.(have convincing OR do not have convincing) evidence to support the hypothesis that the player 9. (made the shot before time expired OR made the shot after the time expired) when the player actually 10. (made the shot before time expired OR made the shot after the time expired) . A Type II error occurs when you 11. (reject OR do not reject) a 12. (True OR False) null hypothesis. In this case, a Type II error corresponds to the referees concluding that they 13. (have convincing OR do not have convincing) evidence to support the hypothesis that the player 14. (made the shot before time expired OR made the shot after the time expired) when the player actually 15. (made the shot before time expired OR made the shot after the time expired) . Provide a correct and error-free solution. Ensure the method is correct, there must be no calculation errors, and the solution is complete and well-framed properly and Don't give direct answers; it must be clear and properly framed and aligned. Avoid using personal pronouns like 'we', 'you', and 'I' in the answer. Give answer as a teacher that you are giving answer to a student and making them understand properly. Don't use Python, please. The solutions will be evaluated based on six key parameters: Relevancy , ensuring closely matches with the question; Completeness , including like calculations, diagrams, procedural steps, & explanatory statements in the solution.; Accuracy, ensuring correctness of concepts and methods; Clarity , assessing readability and simplicity of language; Structure , focusing on organization and presentation; and Voice , determining the response feels natural and human-like rather than robotic. Give a two-line best explanation or interpretation where there is a need for it. Give overall short final answer in last. The complete solution is lacking; please complete the whole answer till the end. Please adhere and strictly follow all these guidelines anyhow. Thank you.) dont use phython

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Asked by: Test User 100106
Created at: 2025-04-28 20:06:15

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Let’s break down the analogy between an instant replay review in sports and the process of hypothesis testing, ensuring clarity and completeness in each step of the reasoning. --- ### **Formulation of Hypotheses in the Sports Context** Suppose the referees originally rule that the last shot was made **before** the clock expired. The opposing coach challenges this call, believing the shot was **after** time expired. The scenario can be mapped onto hypothesis testing as follows: - **Null Hypothesis (H₀):** The player made the shot before time expired. *This reflects the original call—the assumption maintained unless strong evidence suggests otherwise.* - **Alternative Hypothesis (H₁):** The player made the shot after time expired. *This is the claim requiring convincing evidence to overturn the original call.* In a hypothesis test, the process begins with the assumption that the null hypothesis is true. The objective is then to determine whether the evidence is strong enough to reject this assumption in favor of the alternative hypothesis. --- ### **Step-by-Step Filling of the Hypothesis Test Analogy** **1.** The null hypothesis is that the player → **made the shot before time expired.** **2.** The alternative hypothesis is that the player → **made the shot after time expired.** **3.** The testing procedure then assumes that the player → **made the shot before time expired** *(This is the default position, analogous to assuming the null hypothesis is true.)* **4.** The goal is to determine whether there is enough evidence to infer that the player → **made the shot after time expired.** **Interpretation:** This mirrors how scientific studies start by assuming the null hypothesis is true, and only reject it if the evidence is strong enough in favor of the alternative. --- ### **5. Possible Decisions After Reviewing the Video** The referees, after reviewing the evidence, have two decisions analogous to the outcomes of a hypothesis test: - **Reject the null hypothesis:** Conclude there is convincing evidence the original call was incorrect. - **Fail to reject the null hypothesis:** Conclude there is not enough convincing evidence to overturn the original call. The correct choices from the provided options are: - **B.** Conclude that they have convincing evidence to support the hypothesis that the player made the shot after time expired *(This means rejecting the null in favor of the alternative.)* - **E.** Conclude that they do not have convincing evidence to support the hypothesis that the player made the shot after time expired *(This means failing to reject the null hypothesis, so the original call stands.)* **Explanation:** Not rejecting the null does not prove it true; it only indicates insufficient evidence to overturn the original decision. --- ### **Type I and Type II Error Analysis** - **Type I Error:** Occurs when the null hypothesis is **rejected** even though it is **true**. In this context: - The referees conclude that they **have convincing evidence** to support the hypothesis that the player **made the shot after time expired** (rejecting the original call), - when, in reality, the player **made the shot before time expired** (the original call was correct). - **Type II Error:** Occurs when the null hypothesis is **not rejected** even though it is **false**. In this context: - The referees conclude that they **do not have convincing evidence** to support the hypothesis that the player **made the shot after time expired** (failing to overturn the original call), - when, in reality, the player **made the shot after time expired** (the original call was incorrect). --- ### **Filling in the Blanks for Error Types** **Type I error:** - 6. **reject** - 7. **True** - 8. **have convincing** - 9. **made the shot after time expired** - 10. **made the shot before time expired** **Type II error:** - 11. **do not reject** - 12. **False** - 13. **do not have convincing** - 14. **made the shot after time expired** - 15. **made the shot after time expired** --- ### **Summary Table** | Step | Concept | Correct Answer | |------|---------------------------|---------------------------------------------------------------| | 1 | Null hypothesis | made the shot before time expired | | 2 | Alternative hypothesis | made the shot after time expired | | 3 | Assumed true | made the shot before time expired | | 4 | What to infer | made the shot after time expired | | 5 | Possible decisions | B and E | | 6 | Type I: action | reject | | 7 | Type I: null status | True | | 8 | Type I: evidence | have convincing | | 9 | Type I: claim | made the shot after time expired | | 10 | Type I: reality | made the shot before time expired | | 11 | Type II: action | do not reject | | 12 | Type II: null status | False | | 13 | Type II: evidence | do not have convincing | | 14 | Type II: claim | made the shot after time expired | | 15 | Type II: reality | made the shot after time expired | --- ### **Key Interpretations** - **Failing to reject the null hypothesis** (letting the original call stand) does not confirm the original call is correct; it only means the evidence was not strong enough to overturn it. - **Rejecting the null hypothesis** (overturning the original call) should only occur if there is clear and convincing evidence from the replay, analogous to statistical significance in hypothesis testing. - **Type I error** is a “false positive”—overturning a correct call. - **Type II error** is a “false negative”—failing to overturn an incorrect call. --- ### **Final Short Answer** The process of instant replay review in sports closely parallels hypothesis testing: the referees' original call is treated as the null hypothesis, and only clear evidence can overturn it (reject the null). The two possible decisions are either to conclude there is convincing evidence to overturn the call (reject the null in favor of the alternative) or not enough evidence to do so (fail to reject the null). Type I error means wrongly overturning a correct call, while Type II error means failing to overturn an incorrect call.

Question:

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 1. (made the shot before time expired OR made the shot after the time expired), and the alternative hypothesis is that the player 2. (made the shot before time expired OR made the shot after the time expired). The testing procedure then assumes that the player 3. (made the shot before time expired OR made the shot after the time expired) , with a goal of determining whether there is enough evidence to infer that the player 4.(made the shot before time expired OR made the shot after the time expired) . 5. 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? (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.) Check all that apply. A. Conclude that they have convincing evidence to support the hypothesis that the player made the shot before time expired B. Conclude that they have convincing evidence to support the hypothesis that the player made the shot after time expired C. Conclude that they do not have convincing evidence to support the hypothesis that the player made the shot before time expired D. Conclude that the player made the shot before time expired E. Conclude that they do not have convincing evidence to support the hypothesis that the player made the shot after time expired A Type I error occurs when you 6. (reject OR do not reject) a 7. (True OR False) null hypothesis. In this case, a Type I error corresponds to the referees concluding that they 8.(have convincing OR do not have convincing) evidence to support the hypothesis that the player 9. (made the shot before time expired OR made the shot after the time expired) when the player actually 10. (made the shot before time expired OR made the shot after the time expired) . A Type II error occurs when you 11. (reject OR do not reject) a 12. (True OR False) null hypothesis. In this case, a Type II error corresponds to the referees concluding that they 13. (have convincing OR do not have convincing) evidence to support the hypothesis that the player 14. (made the shot before time expired OR made the shot after the time expired) when the player actually 15. (made the shot before time expired OR made the shot after the time expired) .

This is AI generated Response.
Asked by: Test User 100106
Created at: 2025-04-28 20:10:12

Final Answer:

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Let's carefully analyze the scenario and translate it into the language of hypothesis testing, ensuring clarity and precision at each step. --- ### **1. Formulation of Hypotheses** - **Null Hypothesis (H₀):** The player **made the shot before** the time expired. *(This is the original call, assumed true unless proven otherwise.)* - **Alternative Hypothesis (H₁):** The player **made the shot after** the time expired. *(This is the claim that challenges the original call and requires evidence to support.)* --- ### **2. Assumptions in the Testing Process** - The process **assumes** that **the player made the shot before** the time expired, i.e., the null hypothesis is true until evidence suggests otherwise. - The goal is **to determine whether there is enough evidence** to **reject** this assumption and conclude that the shot was **after** the time expired. --- ### **3. Possible Decisions After Evidence Review** **In hypothesis testing, the two possible decisions are:** - **Reject H₀:** Conclude that there is convincing evidence the null hypothesis is false—meaning, the shot was **after** the time expired. - **Fail to reject H₀:** Conclude that there is **not enough convincing evidence** to reject the null hypothesis—meaning, the shot was **before** the time expired, or simply, the original call stands. --- ### **4. Corresponding Choices from the Question** Based on the above, the **correct options** are: - **B.** *Conclude that they have convincing evidence to support the hypothesis that the player made the shot after time expired.* *(Reject the null hypothesis and support the alternative.)* - **E.** *Conclude that they do not have convincing evidence to support the hypothesis that the player made the shot after time expired.* *(Fail to reject the null hypothesis; the original call remains.)* *Note:* It is important to recognize that "not having convincing evidence" does not prove the null hypothesis is true; it simply indicates insufficient evidence to reject it. --- ### **5. Errors in Hypothesis Testing** **Type I Error:** - Occurs when the null hypothesis is **rejected** **when it is actually true**. - In this context: - The referees **reject H₀** (believe the shot was after time expired), - **when in fact**, the shot was **before** time expired. **Therefore:** - **6.** reject - **7.** True - **8.** have convincing - **9.** made the shot after time expired - **10.** made the shot before time expired *This represents a false positive—incorrectly overturning a correct call.* --- **Type II Error:** - Occurs when the null hypothesis is **not rejected** **when it is actually false**. - In this context: - The referees **fail to reject H₀** (do not overturn the call), - **when in fact**, the shot was **after** time expired. **Thus:** - **11.** do not reject - **12.** False - **13.** do not have convincing - **14.** made the shot after time expired - **15.** made the shot after time expired *This represents a false negative—failing to overturn an incorrect call.* --- ### **6. Summary of Correct Fill-ins** | Concept | Correct Fill-in | |------------------------------|----------------------------------------------------------------------------------------------| | Null hypothesis | made the shot before time expired | | Alternative hypothesis | made the shot after time expired | | Assumed true in testing | made the shot before time expired | | Goal of testing | to determine whether there is enough evidence to support that the player made the shot after time expired | | Possible decisions | **B** and **E** | | Type I error (incorrect rejection) | reject, True, have convincing, made shot after, made shot before | | Type II error (incorrect failure to reject) | do not reject, False, do not have convincing, made shot after, made shot after | --- ### **Final Explanation** In essence, the process of reviewing a questionable call in sports is directly analogous to hypothesis testing: the original call acts as the null hypothesis, and the decision to overturn it depends on whether the evidence is strong enough to reject that null. The two main possible outcomes are either to reject the null hypothesis (overturn the call) or to fail to reject it (stand by the original call). Errors in this process are akin to Type I and Type II errors in statistics, where mistakes are made in incorrectly rejecting or failing to reject the null hypothesis based on the evidence

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