Please show all work and write down reasoning ! C Suppose a diagnostic test for

Question

Please show all work and write down reasoning !

C Suppose a diagnostic test for a condition known as Condition X has the following results: test act Yes 20 1 No 80 1899 Here "actual" is whether a person actually has condition X or not, while test is the result of the test or -. 1. What are this test's false positive and false negative rates? 2. What is the percent age of the sample having condition X? 3. Given that a person tests positive, what is her/his probability of having Condition X? 4. Can you explain using the idea of conditional probability?

Explanation / Answer

1) The false positive rate is computed here as:

= Number of false positives / Total number of actual no

= 80 / ( 1899 + 80 )

= 0.0404

The false negative rate is computed here as:

= Number of false negatives / Total number of actual yes

= 1 / ( 20 + 1 )

= 0.0476

2) The percentage of people having condition X is computed here as:

= (20 + 1) / (20 + 1 + 1899 + 80)

= 0.0105

Therefore 1.05% is the required answer here.

3) Given a test is positive, probability of having condition X here is computed as:

= Number of true positives / Number of positives

= 20 / (20 + 80 )

= 0.2

Therefore 0.2 is the required probability here.

4) The given probabilities are computed using the conditional probability condition only.

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