Calculus flashcards

All 20 cards

1. Card 1

   In the context of a court case, what does the null hypothesis represent regarding the person on trial?

   In a court case, the null hypothesis represents that the person is innocent. This is the default assumption that the jury starts with.

2. Card 2

   What does the alternative hypothesis represent in the context of a court case?

   The alternative hypothesis in a court case represents that the person is not innocent, which is equivalent to stating that the person is guilty. This is the claim that needs sufficient evidence to be accepted.

3. Card 3

   Under what condition can the null hypothesis be rejected by a jury in a court case?

   The null hypothesis can only be rejected if there is enough evidence to doubt it. In legal terms, this means the jury can only convict if there is evidence beyond reasonable doubt for the null hypothesis of innocence.

4. Card 4

   What is the primary task of the members of a jury in a court case?

   The primary task of the members of a jury is to decide whether a person is guilty or innocent. This decision is based on the evidence presented to them during the trial.

5. Card 5

   Why might a jury make a mistake in their decision regarding a person's guilt or innocence?

   A jury might make a mistake because they do not know whether the person is really guilty or innocent. Their decision is based on presented evidence, which may not always perfectly reflect the truth.

6. Card 6

   If a jury concludes that there is not enough evidence to doubt the null hypothesis, what is their verdict?

   If a jury concludes that there is not enough evidence to doubt the null hypothesis, their verdict would be that the person is innocent. This means they could not reject the null hypothesis.

7. Card 7

   What is the standard of proof required to reject the null hypothesis of innocence in a court case?

   The standard of proof required to reject the null hypothesis of innocence is 'beyond reasonable doubt.' This high standard ensures that a conviction is only made when there is compelling evidence against the defendant.

8. Card 8

   Explain the concept of 'beyond reasonable doubt' in the context of rejecting the null hypothesis.

   'Beyond reasonable doubt' means that the evidence presented is so convincing that there is no other logical explanation for the facts except that the defendant committed the crime. This level of certainty is required to reject the null hypothesis of innocence.

9. Card 9

   If a jury convicts a person, what does this imply about their assessment of the null hypothesis?

   If a jury convicts a person, it implies that they have found enough evidence to reject the null hypothesis of innocence. They have concluded that the evidence presented proves beyond reasonable doubt that the person is not innocent (i.e., guilty).

10. Card 10

    What is the initial assumption a jury makes about a defendant before any evidence is presented?

    The initial assumption a jury makes about a defendant before any evidence is presented is that the person is innocent. This is the starting point, represented by the null hypothesis.

11. Card 11

    If a court case involves 12 jurors, and 10 of them believe there is enough evidence to reject the null hypothesis, while 2 do not, what is the likely outcome if the standard is unanimous beyond reasonable doubt?

    If the standard is unanimous beyond reasonable doubt, and 2 jurors do not believe there is enough evidence, the null hypothesis of innocence cannot be rejected. The person would likely not be convicted, as unanimity is often required for a guilty verdict.

12. Card 12

    Suppose a prosecutor presents 5 pieces of evidence. If the jury finds 3 pieces to be highly compelling, but 2 pieces are contradictory, leading to 'reasonable doubt,' what decision should they make regarding the null hypothesis?

    Given the presence of contradictory evidence leading to 'reasonable doubt,' the jury should not reject the null hypothesis. The standard for conviction requires evidence beyond reasonable doubt, which is not met if significant doubt exists.

13. Card 13

    A defense attorney successfully casts doubt on every piece of evidence presented by the prosecution. If the jury's role is to decide based on evidence, what is the most probable outcome for the null hypothesis?

    If the defense attorney successfully casts doubt on all evidence, the jury will likely not find enough evidence to reject the null hypothesis. Therefore, the person would be found innocent, as the null hypothesis of innocence stands.

14. Card 14

    Imagine a scenario where 95% of the evidence points to guilt, but a small, unexplained inconsistency remains. If the jury must decide based on 'beyond reasonable doubt,' what is the implication for rejecting the null hypothesis?

    Even with 95% of evidence pointing to guilt, if a 'small, unexplained inconsistency' creates reasonable doubt, the jury might not be able to reject the null hypothesis. The standard of 'beyond reasonable doubt' means even a small, reasonable doubt can prevent conviction.

15. Card 15

    A jury is presented with evidence that has a 1 in 100,000 chance of occurring if the person were innocent. If they must decide based on 'beyond reasonable doubt,' what is the strength of this evidence for rejecting the null hypothesis?

    This evidence is very strong for rejecting the null hypothesis, as a 1 in 100,000 chance of occurrence if innocent suggests an extremely low probability of innocence. This would likely meet the 'beyond reasonable doubt' standard for conviction.

16. Card 16

    If a jury is 80% confident that a person is guilty, but the legal standard requires 'beyond reasonable doubt' (often interpreted as 95-99% confidence), what decision should they make regarding the null hypothesis?

    If the jury is only 80% confident, they should not reject the null hypothesis. The 80% confidence level falls short of the 'beyond reasonable doubt' standard, meaning there is still reasonable doubt about guilt.

17. Card 17

    A jury hears testimony from 3 witnesses. Witness A is highly credible, Witness B is somewhat credible, and Witness C is not credible. How does the varying credibility of witnesses affect the jury's ability to gather 'enough evidence' to reject the null hypothesis?

    The varying credibility directly impacts the weight of evidence. Highly credible testimony strengthens the case for rejecting the null, while non-credible testimony weakens it or introduces doubt. The jury must weigh all testimonies to determine if 'enough evidence' exists beyond reasonable doubt.

18. Card 18

    If a jury makes a Type I error in a court case, what mistake have they made in terms of the null hypothesis and the person's actual guilt?

    If a jury makes a Type I error, they have incorrectly rejected the null hypothesis. This means they have convicted an innocent person, concluding the person is not innocent when in reality they are innocent.

19. Card 19

    If a jury makes a Type II error in a court case, what mistake have they made in terms of the null hypothesis and the person's actual guilt?

    If a jury makes a Type II error, they have failed to reject the null hypothesis when it was false. This means they have acquitted a guilty person, concluding the person is innocent when in reality they are guilty.

20. Card 20

    Consider a case where the prosecution presents 10 pieces of evidence, and the defense successfully refutes 7 of them. If the remaining 3 pieces are circumstantial, what is the likelihood of the jury rejecting the null hypothesis of innocence?

    Given that 7 pieces of evidence were refuted and the remaining 3 are circumstantial, it is highly unlikely the jury will reject the null hypothesis. Circumstantial evidence alone, especially with a significant portion of the prosecution's case dismantled, rarely meets the 'beyond reasonable doubt' standard.

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