A new? lie-detector test has been devised and must be tested before it is put into...

A new? lie-detector test has been devised and must be tested before it is put into use. Three hundred people are selected at? random, and each person draws and keeps a card from a box of 300 cards. Half the cards instruct the person to lie and the others instruct the person to tell the truth. Of those who? lied, 70?% fail the new? lie-detector test? (that is the test indicated? lying). Of those who told the? truth, 5?% failed the test.

What is the probability that a randomly chosen subject will have lied given that the subject failed the? test? That the subject will not have lied given that the subject failed the? test?

Solutions

Expert Solution

Based on given data, the contigency table is created as below,

	Lie	Do not Lie	Total
Fail the test (test indicated? lying)	105	7.5	112.5
Do not fail the test (test do not indicate lying)	45	142.5	187.5
Total	150	150	300

Total persons who lie = Total persons who do not lie (tell truth) = 150

Of those who? lied, 70?% fail the new? lie-detector test?.

Then, total persons who lied and fail the test = 150 * 0.7 = 105

and total persons who lied and do not fail the test = 150 - 105 = 45

Of those who told the? truth, 5?% failed the test.

Then, total persons who do not lied and fail the test = 150 * 0.05 = 105

and total persons who do not lied and do not fail the test = 150 - 7.5 = 142.5

Total persons who fail the test = 105 + 7.5 = 112.5

Total persons who do not fail the test = 45 + 142.5 = 187.5

Probability that a randomly chosen subject will have lied given that the subject failed the? test = 105 / 112.5 = 0.9333

Probability that a randomly chosen subject will not have lied given that the subject failed the? test = 7.5 / 112.5 = 0.0667

orchestra answered 1 year ago

Next > < Previous

Related Solutions

A new lie-detector test has been devised and must be tested before it is put into...

A new lie-detector test has been devised and must be tested before it is put into use. 200 people are selected at random, and each person draws and keeps a card from a box of 200 cards. Half the cards instruct the person to lie and the others instruct the person to tell the truth. Of those who lied, 85% fail the new lie-detector test (that is the test indicated lying). Of those who told the truth, 5% failed the...

A new lie-detector machine is invented and tested. When test subjects lie, the machine catches 86%...

A new lie-detector machine is invented and tested. When test subjects lie, the machine catches 86% of them in a lie. When test subjects tell the truth, the machine thinks that 6% of them lie. A local police department begins to use this lie-detector machine in interrogations. Suppose that 15% of people arrested lie in their interrogations. The police interrogated a subject and the machine indicated that the person was telling the truth. What is the probability that the subject...

suppose a police detective is about to administer a polygraph (lie detector) test on an "individual...

suppose a police detective is about to administer a polygraph (lie detector) test on an "individual of interest" . when a polygraph is administered to an individual who is lying, the chance that the test detects that the individual is lying is 90%. additionally, when polygraph test is administered to an individual who is telling the truth, the chance that the test indicates that the individual is not lying is 84%. finally, the police detective knows that "individuals of interest"...

Imagine that someone has just devised a new muscular endurance test. What would you do to...

Imagine that someone has just devised a new muscular endurance test. What would you do to prove that it is a valid test? (Show all steps, including evaluative ones.)

Sally is a new patient to the clinic and has just tested posative pregnacy test. Her...

Sally is a new patient to the clinic and has just tested posative pregnacy test. Her freind andrea is an employee of the medical clinic and ran into sally and her hsband at the store. andrea congradualtes her freind sally and her husband on the pregnancy. Little did andrea know that sally and her husband been having marital problems and been sleeping in seperte roomswhat did andrea do wrong and how should she have approached sally and her husband?

Before going to the market, a pregnancy test has been applied to a population of 10,000...

Before going to the market, a pregnancy test has been applied to a population of 10,000 women from which 300 were actually pregnant. Suppose this new product returns a “yes” result 99.5 % of the cases in which the person was actually pregnant and 98% of the cases returns a “no” result when the person was not pregnant. Now that the test is in the market: what is the probability that a random user (a women) of the test is not pregnant...

A 10-year-old female has tested positive for the sweat-test and has been diagnosed with cystic fibrosis....

A 10-year-old female has tested positive for the sweat-test and has been diagnosed with cystic fibrosis. Phases: primary, secondary, and tertiary. What phase is cystic fibrosis? What would be a nursing intervention for a 10-year-old with cystic fibrosis?

Weka Company Ltd has been considering the criteria that must be met before a capital expenditure...

Weka Company Ltd has been considering the criteria that must be met before a capital expenditure proposal can be included in the capital expenditure programme. The screening criteria established by management are as follows: No project should involve a net commitment of funds for more than four years. Accepted proposals must offer a time adjusted or discounted rate of return at least equal to the estimated cost of capital. Present estimates are that cost of capital is 15 percent per...

A new test has been developed for diagnosing Rheumatoid Arthritis. The test was evaluated in four...

A new test has been developed for diagnosing Rheumatoid Arthritis. The test was evaluated in four communities with the following results Table-1: Table 1: Results of a new screening test for Rheumatoid Arthritis in Four Communities Community A Rheumatoid Arthritis Present Absent Total Test Result + 887 888 1775 Test Result -- 99 7989 8088 986 8877 9863 Community B Rheumatoid Arthritis Present Absent Total Test Result + 1485 385 1870 Test Result -- 165 3465 3630 1650 3850...

A new, simple test has been developed to detect a particular type of cancer. The test...

A new, simple test has been developed to detect a particular type of cancer. The test must be evaluated before it is put into use. A medical researcher selects a random sample of 1,000 adults and finds (by other means) that 3% have this type of cancer. Each of the 1,000 adults is given the test, and it is found that the test indicates cancer in 97% of those who have it and in 2% of those who do not....

Subjects