problem 1:A polygraph examiner is judging the guilt or innocence of 280 people c

Question

problem 1:A polygraph examiner is judging the guilt or innocence of 280 people charged with a crime, 140 of whom are known to be innocent and 140 of whom are known to be guilty (but the polygrapher doesn’t know who’s who). In the table are the outcomes:

True Status

Innocent Guilty

Polygraph Result Acquitted 131 15

Convicted 9 125

Calculate the Type I and Type II error rates for this polygrapher.

problem 2: You want to determine whether a coin is ‘fair’, i.e., whether its probability of coming up heads is 1/2. You toss it 200 times and it comes up heads 84 times. This is a bit lower than you’d expect from a fair coin, but does it suggest the coin is not fair? Let’s find out:

(a) Describe the null hypothesis H0 in a short sentence.

(b) Describe the alternative hypothesis H1 in a short sentence.

(c) Decide whether this evidence leads you to reject H0. Use a significance level = 0.05

Explanation / Answer

problem 1:A polygraph examiner is judging the guilt or innocence of 280 people charged with a crime, 140 of whom are known to be innocent and 140 of whom are known to be guilty (but the polygrapher doesn’t know who’s who).

Here,

Ho: Person is not guilty.
Ha: Person is guilty.

Hence, a type I error is convicting an innocent person.

Hence,

P(type I) = 9/140 = 0.064285714 [ANSWER]

*************************

Hence, a type II error is acquitting a guilty person. Hence,

P(type II) = 15/140 = 0.107142857 [ANSWER]

*******************************************

Hi! Please submit the next part as a separate question. That way we can continue helping you! Please indicate which parts are not yet solved when you submit. Thanks!

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.