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Answer:
D. AB/CE = ED/BC
Step-by-step explanation:
In this question you apply the side-Angle-side similarity property that makes the two right triangles similar.
In this property, the lengths of the corresponding legs of the two right triangles are proportional.
Hence
Leg AB corresponds to leg CE
Leg ED corresponds to leg BC
From the property;
An actual two-by-two table is a tabular representation containing two rows and two columns.
- The columns consist of the tested True positive for prostate cancer and tested True Negative for prostate cancer
- The rows consist of the predicted positive screening and predicted negative values
Mathematically, the set-up of the two-by-two table for this data can be computed as:
Tested True Positive for cancer True Negative Total
Predicted Positive 800 3200 4000
Predicted Negative 100 95900 96000
Total 900 99100 100000
<h3>b)</h3>The prevalence rate of prostate cancer in this population is:
= 9 per thousand.
<h3>c)</h3>
The calculation of the sensitivity of this screening is as follows:
where;
- TP = True positive for cancer
- PN₁ = Predicted Negative for true positive cancer
∴
= 0.889
= 88.9%
The interpretation shows that 88.9% are correctly identified to be actual positive for prostate cancer.
<h3>d)</h3>The calculation of the specificity of this screening is as follows:
where;
- TN = True positive for cancer
- PN₂ = Predicted Negative for true negative cancer
∴
= 0.9677
= 96.77%
The interpretation shows that 96.7% of an actual negative is correctly identified as such.
<h3>e)</h3>
The positive predicted value of the screening test is computed as:
= 0.2
= 20%
The interpretation of the positive predicted value of this screening shows that 20% that are subjected to the diagnosis of positive prostate cancer truly have the disease.
Learn more about tabular representation here: