A new, non-evasive, test is to indicate the existance of colorectal cancers in patients who have...
A new, non-evasive, test is to indicate the existance of colorectal cancers in patients who have colorectal cancer with a probability of 0.95. However, this test will also show the presense of colorectal cancer in patients who do not have colorectal cancer 22% of the time.
The chance that a person taking this test has colorectal cancer is 0.09
Find the sensitivity of this test. Use two decimals.
b. Find the specificity of this test. Use two decimals.
c. A person taking this test has tested positive for colorectal cancer. What is the probability he/she has colorectal cancer? Use four decimals.
d. What is the probability that the person in part c does not have colorectal cancer? Use four decimals.
Homework Answers
a) sensitivity of this test =P(tested positive|have disease) =0.95
b) specificity of this test =P(tested negative |not have disease) =1-0.22 =0.78
c)
| P(tested positive)=P(have disease and tested positive)+P(not have disease and tested positive) | ||||||
| =0.09*0.95+0.91*0.22=0.2857 | ||||||
| Therefore P(have disease|tested positive)=0.09*0.95/0.2857=0.2993 |
d)
P(not have disease given tested positive) =1-P(have disease|tested positive) =1-0.2993 =0.7007
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