Question

2 fill in the blank 13 points fill out the table above using the following clues based on scientific statics for this screening test. • 450 patients were tested • 50 of the patients had the disease • the false negative rate was 2% • the false positive rate was 10.25% based on your answers in the table above, calculate the following statistics. (i recommend that you check your work above before you use those numbers for this problem.) what is the sensitivity of the test? choose your answer. what is the specificity of the test? choose your answer... if a patient tests positive, whats the probability theyre actually infected? choose your answer... if a patient tests negative, whats the probability theyre actually not infected? choose your answer...

Explanation:

Step1: Calculate true - positive and false - negative

The number of infected patients is 50. The false - negative rate is 2%. So the number of false - negatives is $50\times0.02 = 1$. Then the number of true - positives is $50 - 1=49$.

Step2: Calculate false - positive and true - negative

The number of non - infected patients is $450 - 50 = 400$. The false - positive rate is 10.25%. So the number of false - positives is $400\times0.1025 = 41$. Then the number of true - negatives is $400-41 = 359$.

Step3: Fill in the contingency table

	Not Infected	Infected	Total
Positive	41	49	90
Total	400	50	450

Step4: Calculate sensitivity

Sensitivity (true - positive rate) is $\frac{\text{True Positives}}{\text{Infected}}=\frac{49}{50}=0.98$ or 98%.

Step5: Calculate specificity

Specificity (true - negative rate) is $\frac{\text{True Negatives}}{\text{Not Infected}}=\frac{359}{400}=0.8975$ or 89.75%.

Step6: Calculate positive predictive value

Positive predictive value (probability of being infected given a positive test) is $\frac{\text{True Positives}}{\text{Positive}}=\frac{49}{90}\approx0.5444$ or 54.44%.

Step7: Calculate negative predictive value

Negative predictive value (probability of not being infected given a negative test) is $\frac{\text{True Negatives}}{\text{Negative}}=\frac{359}{360}\approx0.9972$ or 99.72%.

Answer:

Sensitivity: 98%
Specificity: 89.75%
Probability of being infected given a positive test: 54.44%
Probability of not being infected given a negative test: 99.72%