1. A polygraph examiner is judging the guilt or innocence of 280 people charged
ID: 3154161 • Letter: 1
Question
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
Polygraph Result
Acquitted = Innocent: 131 Guilty: 15
Convicted = Innocent: 9 Guilty: 125
Calculate the Type I and Type II error rates for this polygrapher.
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
1.
Note that by default, a person is not guilty.
Hence:
Ho: Person is innocent.
Ha: Person is guilty.
Hence, as a type I error is incorrectly rejecting Ho,
P(type I) = P(Convicted|Innocent) = 9/140 = 0.064285714 [ANSWER]
Also, as a type II error is incorrectly failing to reject Ho,
P(Type II) = P(Acquitted|Guilty) = 15/140 = 0.107142857 [ANSWER]
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