A school nurse examined a population of 1,000 children in an attempt to detect h
ID: 3172559 • Letter: A
Question
A school nurse examined a population of 1,000 children in an attempt to detect hearing impairment. The prevalence of a hearing impairment in this population is known to be 20%. The sensitivity of the examination is 50% and its specificity is 80%. All children labeled as “positive” (i.e., suspected of having a hearing impairment) by the school nurse are sent for further examination by an audiologist. The sensitivity of the audiologist’s examination is 98% and its specificity is 90%. How many children are labeled “positive” by the school nurse? a. 100 b. 360 c. 260 d. 160 e. 420 A school nurse examined a population of 1,000 children in an attempt to detect hearing impairment. The prevalence of a hearing impairment in this population is known to be 20%. The sensitivity of the examination is 50% and its specificity is 80%. All children labeled as “positive” (i.e., suspected of having a hearing impairment) by the school nurse are sent for further examination by an audiologist. The sensitivity of the audiologist’s examination is 98% and its specificity is 90%. How many children are labeled “positive” by the school nurse? a. 100 b. 360 c. 260 d. 160 e. 420 A school nurse examined a population of 1,000 children in an attempt to detect hearing impairment. The prevalence of a hearing impairment in this population is known to be 20%. The sensitivity of the examination is 50% and its specificity is 80%. All children labeled as “positive” (i.e., suspected of having a hearing impairment) by the school nurse are sent for further examination by an audiologist. The sensitivity of the audiologist’s examination is 98% and its specificity is 90%. How many children are labeled “positive” by the school nurse? a. 100 b. 360 c. 260 d. 160 e. 420Explanation / Answer
PV+ = true positive/(true positive + false positive)
Predictive value for a negative result (PV-):
PV- aks " If f the test result is negative what is the probability that the patient does not have disease?"
PV - = true negatives/(true negatives +false negatives)
Note that the prevalence of hearinf impairment in the population is 20%
1) The disease prevalence,the percentage of the population that is truly diseased, is 20/100 =x/1000
that is x = 200
2. The sensitivity is the percentage of truly diseased individuals who correctly receive a positive test result. Therefore, the sensitivity is 50/100 = y/200
that is y = 100
3. The specificity is the percentage of truly healthy individuals who correctly receive a negative test result. Therefore, the specificity is 80/100 = z/800
that is z = 640
4. The positive predictive value is the percentage of people who receive a positive test that truly have the disease. Therefore, the positive predictive value is 100/260 = 0.3846 or 38.46%.
Hence number of chidren which are labelled +ve by the school nurse are 260
Option C is correct.
Specificity: Specificity = true negatives / (true negative + false positives)
Predictive value for a positive result (PV+):
PV+ asks " If the test result is positive what is the probability that the patient actually has the disease?"
PV+ = true positive/(true positive + false positive)
Predictive value for a negative result (PV-):
PV- aks " If f the test result is negative what is the probability that the patient does not have disease?"
PV - = true negatives/(true negatives +false negatives)
Note that the prevalence of hearinf impairment in the population is 20%
1) The disease prevalence,the percentage of the population that is truly diseased, is 20/100 =x/1000
that is x = 200
2. The sensitivity is the percentage of truly diseased individuals who correctly receive a positive test result. Therefore, the sensitivity is 50/100 = y/200
that is y = 100
3. The specificity is the percentage of truly healthy individuals who correctly receive a negative test result. Therefore, the specificity is 80/100 = z/800
that is z = 640
4. The positive predictive value is the percentage of people who receive a positive test that truly have the disease. Therefore, the positive predictive value is 100/260 = 0.3846 or 38.46%.
predicted condition +ve predicted condition -ve total condition +ve y=100 200-100 = 100 x=200 condition -ve 800-640=160 z=640 1000-200=800 total 100+160=260 100+640 = 740 1000Hence number of chidren which are labelled +ve by the school nurse are 260
Option C is correct.
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