f) what is the negative predictive value of the test? Hypothetical results from

Question

f) what is the negative predictive value of the test? Hypothetical results from 10,000 mammograms for women with tumors: a) What is the baseline rate of malignancy? (percent form) b) What is the false negative rate? (percent form) c) What is the false positive rate? (percent form) d) What is the probability that a mammogram is positive if a woman has a malignant tumor? (decimal form) e) What is the probability that a woman has a malignant tumor if her mammogram is positive? That is, what is the positive predictive value of the test? (decimal form - 3 decimal places)

Explanation / Answer

Answer to part a)

the baseline rate of malignancy is = 1075/10000 = 0.1075

Thus the baseline rate = 0.1075 *100 = 10.75%

.

Answer to part b)

tumor in harmful rate is present is 15 such people who are tested negative , this is the number of people with false neagtive

Thus false negative rate = 15/10000 = 0.0015

Thus false negative rate = 0.0015*100 = 0.15%

.

Answer to part c)

tumor in benign state, still the test shows positive = 990 cases are there

Thus the false positive rate is = 990/10000 = 0.0990

False positive rate = 0.0990 *100 = 9.90%

.

Answer to part d)

There are 100 women with malignant tumor and out of them 85 tested positive

Thus P = 85/100 = 0.85

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