Question

Errors in Hypothesis Testing and Criminal Court Trials A criminal court trial is rife with hypothesis test errors. The person charged with committing criminal activity (the defendant) must prove his or her innocence or be sentenced to serve time in prison. Given that in the United States a person is assumed innocent until proven guilty, the null hypothesis (Ho) and alternative hypothesis (Ha) for a criminal court trial can be expressed as follows: Ho: The defendant is innocent. Ha: The defendant is guilty. Careful rscords regarding the verdicts in criminal court trials are maintained by statisticians who work in the criminal justice area in order to infer whether or not changes need to be mada regarding the significance level (a) for hypothesis tests on the lio and Ha given atove. Questions A. If too many truly innocent defendants are found guilty, should the level of α be set closer tops or closer to 10%? Why?irr B. If too many truly guilty defendants are found not guilty, should the level of a be set closer to 1 % or closer to10%? Why? Hint: Determine the Type I and Type II errors for this situation.

Hi guys please assist me answering the above questions in detailed. Thank you!

Answer 1

type i error - reject the null hypothesis when it is true
that is concluding a defendant guilty when they are not

type ii error - fail to reject the null hypothesis when it is false

we fail to conclude that a defendant is guilty when they are actually guilty

alpha = type i error
a)
we have to reduced type i error
hence alpha = 0.01

b)
we have to reduce type ii error

Decreasing alpha increases the chance of a Type II error

hence alpha = 0.10