Read “Juries in High-Profile Cases…” a. Juries are sequestered to keep them from
ID: 3338911 • Letter: R
Question
Read “Juries in High-Profile Cases…”
a. Juries are sequestered to keep them from being influenced by anything other than the evidence presented in court. If jurors were allowed to watch TV, and media sources focused their coverage on evidence that indicated guilt in a particular case, how would this affect the jurors’ decision? Treat the decision as a statistical one and use the p-value approach.
b. In criminal cases, jurors are told that they can only find the defendant guilty if they are convinced "beyond a reasonable doubt" of his or her guilt. In civil cases, only a “preponderance of the evidence” is required to convict a defendant. What type of error is a judge trying to avoid in criminal cases? Why are they more concerned about this error in criminal cases?
c. What is the effect of the “beyond a reasonable doubt” rule on the power of the hypothesis test?
Explanation / Answer
a)
if the media is going to indicate guilt in a particular case, they are going towards establishing alternate hypothesis. That is the media is saying there is significant evidence for conviction.
In the first case when the null hypothesis is true (no significant evidence), media is forcing the judge to say there is significant evidence. Meaning they are trying to decrease the p-value so that he can reject null hypothesis and say there is significant evidence.
in the second case, when the null hypothesis is false (there is significant evidence), media is forcing the judge to say there is significant evidence. meaning they are trying to decrease the already low p-value so that he can reject null hypthoseis and say there is significant evidence.
In the first case, media is not getting it right by decreasing the p-value (which is high in real case)
In the second case, media is getting it right by further decreasing the p-value (which is low is real case)
b)
In criminal cases only so much evidence is required to convict a defendant.
type 1 error is incorrect rejection of true null hypothesis. That is when the null hypothesis is true (no guilt), we infer that there is significant evidence.
type 2 error is incorrectly retaining false null hypothesis. That is when the null hypothesis is false (there is guilt) we infer that there is no significant evidence.
In this case the error that the judge is trying to avoid is type 2 error. The judge convicts the defendant, so that the defendant doesn't go scott-free when there is even minor evidence to suggest guilt.
c)
power = 1- beta
power is the probabilty of rejecting a false null hypothesis. It is inversely related to beta (beta - the probability of making type 2 error)
Beyond a reasonable doubt means alpha is less than 0.05 or 0.01, that is the probability of making type 1 error is less than 5% or 1% or clost to 0%.
Beyond reasonable doubt means the probability of type 1 is 0% (ok, may be almost close to 0). There is significant evidence.
When power is high, that means the probability of rejecting false null hypothesis is high,
that is when there is evidence (false null hypothesis), the probability of rejecting is high.
So we can say beyond reasonable doubt means very high power.
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