Explain how a court trial is like hypothesis testing. Write the hypotheses, explain a Type 1 and Type 2 error, and explain why a verdict is “not guilty” instead of innocent.(a) Write the hypotheses Ho and Ha in words.Ho: The defendant is guiltyHo: The probability defendant is innocent is lowHo: The probability defendant is innocent is highHo: The defendant is innocent Ha: The defendant is innocentHa: The probability defendant is innocent is lowHa: The defendant is guiltyHa: The probability defendant is innocent is high(b) What is a Type 1 Error in a court trial?You fail to reject Ho, but you should have. You send an innocent person to prison.You reject Ho, but you should not have. You let a guilty person go free.You fail to reject Ho, but you should have. You let a guilty person go free.You reject Ho, but you should not have. You send an innocent person to prison.(c) What is a Type 2 Error in a court trial?You reject Ho, but you should not have. You let a guilty person go free.You fail to reject Ho, but you should have. You send an innocent person to prison.You reject Ho, but you should not have. You send an innocent person to prison.You fail to reject Ho, but you should have. You let a guilty person go free.(d) A jury convicts if "beyond a reasonable doubt" they believe the defendant is guilty. This is analogous to making αα smaller or larger?It is analogous to making αα larger because a large αα means there is a small probability of a Type 2 error.It is analogous to making αα smaller because a small αα means there is a small probability of a Type 2 error.It is analogous to making αα smaller because a small αα means there is a small probability of a Type 1 error.It is analogous to making αα larger because a large αα means there is a small probability of a Type 1 error.(e) Why does the jury say the defendant is "not guilty"?The jury accepts the defendant's innocence as truth.The jury is not confident in the person's innocence. They are simply not convinced of the alternative hypothesis that the person is guiltyThe significance level in the hypothesis test was not low enough.The jury is not confident in the person's innocence. They are simply not convinced of the null hypothesis that the person is guilty

Answered: Explain how a court trial is like…

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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Explain how a court trial is like hypothesis testing. Write the hypotheses, explain a Type 1 and Type 2 error, and explain why a verdict is “not guilty” instead of innocent.

(a) Write the hypotheses Ho and Ha in words.

Ho: The defendant is guilty
Ho: The probability defendant is innocent is low
Ho: The probability defendant is innocent is high
Ho: The defendant is innocent

Ha: The defendant is innocent
Ha: The probability defendant is innocent is low
Ha: The defendant is guilty
Ha: The probability defendant is innocent is high

(b) What is a Type 1 Error in a court trial?

You fail to reject Ho, but you should have. You send an innocent person to prison.
You reject Ho, but you should not have. You let a guilty person go free.
You fail to reject Ho, but you should have. You let a guilty person go free.
You reject Ho, but you should not have. You send an innocent person to prison.

You reject Ho, but you should not have. You let a guilty person go free.
You fail to reject Ho, but you should have. You send an innocent person to prison.
You reject Ho, but you should not have. You send an innocent person to prison.
You fail to reject Ho, but you should have. You let a guilty person go free.

(d) A jury convicts if "beyond a reasonable doubt" they believe the defendant is guilty. This is analogous to making αα smaller or larger?

It is analogous to making αα larger because a large αα means there is a small probability of a Type 2 error.
It is analogous to making αα smaller because a small αα means there is a small probability of a Type 2 error.
It is analogous to making αα smaller because a small αα means there is a small probability of a Type 1 error.
It is analogous to making αα larger because a large αα means there is a small probability of a Type 1 error.

(e) Why does the jury say the defendant is "not guilty"?

The jury accepts the defendant's innocence as truth.
The jury is not confident in the person's innocence. They are simply not convinced of the alternative hypothesis that the person is guilty
The significance level in the hypothesis test was not low enough.
The jury is not confident in the person's innocence. They are simply not convinced of the null hypothesis that the person is guilty

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