Question

type the correct answer in each box. use numerals instead of words. a new test is developed to test for organic matter in soil samples, giving \positive\ or
egative\ results to indicate that a sample does or does not contain organic matter. for a soil sample that contains organic matter, the test will give a positive result 95% of the time and a negative result (false negative) 5% of the time. for a soil sample that does not contain organic matter, the test will give a positive result (false positive) 20% of the time and a negative result 80% of the time. a study included a population of 1,000 soil samples, and 70% of those studied where known to contain organic matter. fill in the missing values in the table and statement below. if necessary, round the percentage to one decimal place.

	contains organic matter	does not contain organic matter
positive result	665	blank
negative result	blank	240

if a soil sample test gives a positive result, it is blank % likely that the soil sample contains organic matter.

Explanation:

Step1: Calculate number of false - positives

The number of samples that do not contain organic matter is 300. The false - positive rate for samples without organic matter is 20%. So the number of false - positives is $300\times0.2 = 60$.

Step2: Calculate number of true - positives

The number of samples that contain organic matter is 700. The true - positive rate for samples with organic matter is 95%. So the number of true - positives is $700\times0.95=665$.

Step3: Calculate number of false - negatives

The number of samples that contain organic matter is 700. The false - negative rate for samples with organic matter is 5%. So the number of false - negatives is $700\times0.05 = 35$.

Step4: Calculate number of true - negatives

The number of samples that do not contain organic matter is 300. The true - negative rate for samples without organic matter is 80%. So the number of true - negatives is $300\times0.8=240$.

Step5: Calculate probability that a soil sample contains organic matter given a positive result

The total number of positive results is the sum of true - positives and false - positives, which is $665 + 60=725$. The number of true - positives is 665.
The probability $P=\frac{665}{725}\approx0.917$.

Answer:

0.9