A National Research Council study in 2002, headed by Stephen Fienberg from Carne

Question

A National Research Council study in 2002, headed by Stephen Fienberg
from Carnegie Mellon University, found that lie-detector results are “better than chance, but well
below perfection.” Typically, 80% of the time, the test will conclude someone is a spy and the test
will be right. However, 16% of the time, the test will conclude someone is a spy
and test will be wrong.
1. What is the probability of committing a Type I Error?
2. What would be the consequences of committing a Type I Error?
3. What is the probability of committing a Type II Error?
4. What would be the consequences of committing a Type II Error?

Explanation / Answer

(1) Here null hypothesis is that someone is no spy and alternative hypothesis which shall be proved by lie detector that someone is spy.

Here in this case Type I error is when we wrongly reject the null hypothesis that means that someone is not spy but we accept that he is a spy.

Pr(type I error) = 0.16

Question 2. There will be a very serious mistake because a spy's punishment is death so there will be 20% chance that a person who is not a spy will be called as spy and will be punished.

Question 3

Here type II error means that we fail to reject the null hypothesis that means that the guy is a spy but we couldn't prove it so we have to let him/her go.

Pr(Type II error ) = 1 - 0.80 = 0.20

Question 4. This type II error consequences are also very dangerous as the spy will beset free and now he/ she can perform any anti-national activities.

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