Please, Answers the questions from #1 TO #3. Thank you!!

#1

Polygraph lie-detector machines are commonly used in criminal investigations. The device measures nervous excitement, operating on the idea that if a person is telling the truth they will remain calm.

• The American Polygraph Association claims that polygraphs accurately identify liars 90% of the time. In other words, if a person lied the test results will be positive 90% of the time.
• Although the polygraph test is good at identifying liars, there is a 50% chance that the polygraph test will say a truthful person is lying.

A police force wants to predict the accuracy of lie-detector tests for 1,000 suspected criminals. Assume that 700 per 1,000 suspected criminals tell the truth during polygraph tests.

	Lie	Truth	Row Totals
Test result: negative	P
Test result: postive		Q
Column Totals			1,000

Barber, N. (2013). Do Lie Detectors Work?Psychology Today.

What is the value ofP?

10

30

70

270

#2

For many years the only way to test if a person had tuberculosis (TB) required a laboratory procedure that could take up to several weeks to produce a definite result. There are now DNA-based tests to detect TB that can be done in a couple of hours.

We have the following data on a DNA test for TB

• If a person does not have TB then the DNA test always is negative.
• If a person does have TB, then the DNA test will be positive 94% of the time.

Assume that we will use the test in Africa where the rate of incidence of TB is 450 per 100,000.

	Has TB	Does not have TB	Row Totals
Test result: negative
Test result: postive	P
Column Totals		Q	100,000

What is the probability of a false negative test result? A false negative is P(TB given a negative test).

27 out of 99,577

27 out of 100,000

27 out of 450

423 out of 100,000

#3

For many years the only way to test if a person had tuberculosis (TB) required a laboratory procedure that could take up to several weeks to produce a definite result. There are now DNA-based tests to detect TB that can be done in a couple of hours.

We have the following data on a DNA test for TB

• If a person does not have TB then the DNA test always is negative.
• If a person does have TB, then the DNA test will be positive 94% of the time.

Assume that we will use the test in Africa where the rate of incidence of TB is 450 per 100,000.

	Has TB	Does not have TB	Row Totals
Test result: negative
Test result: postive	P
Column Totals		Q	100,000

What is the value ofQ?

What is the value of Q?

99,550

99,577

450