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Tagged: False Positive Table, probability, Two Way Table
A test for tuberculosis was conducted on 100 people. The results are shown in the table.
a. Describe what a false positive result is.
b. How many people had a false positive result?
c. What percentage of these people had accurate result?
d. What percentage of the people who had a negative test result actually had the disease?
a. A false positive is when the test result incorrectly indicates you have the disease, when you don’t
b. A false positive would be the not accurate people without the disease: 6
c. accurate result = 92 out of 100
^{92}/_{100 }× 100
= 92%
d. The people who had a negative test result include the people with the disease who had a not accurate (2) and the people without the disease who had an accurate (88).
Out of these 90 people, only 2 actually had the disease: ^{2}/_{90 }× 100 = 2.2%
The twotable below shows the results of a new lie detector which is used by NSW police in conjunction with random breathe testing.
Detector Results


Told the Truth

Lied

Total


Accurate Result Inaccurate Result 

250
33 

Total 
175

108

283

What percentage of people who did tell the truth were told they lied?
The people who told the truth would be those that were told they told the truth and had an accurate result = 154
Those who were told they lied and had an inaccurate result = 12
total who told the truth = 166
The percentage that were told they lied would be = $$\frac{12}{166}\times 100$$
= 7.2%
A new test has been developed for determining whether or not people are carriers of the Gaussian virus. A two way table was used to record the results.
Test Results


Positive

Negative

Total


Carrier Not Carrier 

88
112 

Total 
90

110

a. How many people were tested?
b. A person selected from the group is not a carrier of the virus. What is the probability that the test results would show this?
c. For how many of the people tested were their test results accurate?
a. total = 88 + 112
= 200
b. there are 112 people that are not carriers, out of those 96 have a negative result – ie showing they are not a carrier
P = $$\frac{96}{112}$$
= $$\frac67$$
c. an accurate result would mean:
carrier receiving a positive result = 74
non carrier receiving a negative result = 96
accurate = 74 + 96
= 170