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goblinko [34]
3 years ago
12

How to solve a quotient rule problem with a negative in the denominator?

Mathematics
1 answer:
denpristay [2]3 years ago
8 0
You can take the -1 times the final answer and keep the denominator as positive, or keep track of all the negatives.
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predictive value of a positive test = 18.18%

predictive value of a negative test = 94.03%

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Specificity = 70% = 0.7

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True Negative = TN

False Negative = FN

Sensitivity = \frac{TP}{TP + FN} \\0.6 = \frac{TP}{TP + FN} \\0.6TP + 0.6FN = TP\\0.4TP = 0.6FN\\TP = 1.5 FN

Specificity = \frac{TN}{TN + FP} \\0.7 = \frac{TN}{TN + FP} \\0.7TN + 0.7FP = TN\\0.7FP = 0.3 TN\\TN  = 7/3 FP

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30 = 1.5 FN + FN

30 = 2.5 FN

FN = 30/2.5

FN = 12

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TP = 18

FP + TN = T_{total} - T_{disease} \\FP + TN = 300 - 30\\FP + TN = 270\\FP + \frac{7}{3} FP = 270\\\frac{10}{3} FP = 270\\FP = 27 * 3\\FP = 81

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To calculate the Predictive value of positive test (PPT)

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PPT = \frac{TN}{FN + TN} * 100\\PPT = \frac{189}{189+12} * 100\\PPT = \frac{189}{201} * 100\\PPT = 94.03 \%

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