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
negative result	240

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

Explanation:

Step1: Calculate true - positive and false - positive numbers

The number of samples with organic matter is $700$. The test gives a positive result for $95\%$ of samples with organic matter, so the number of true - positives is $0.95\times700 = 665$. The number of samples without organic matter is $300$. The test gives a positive result for $20\%$ of samples without organic matter, so the number of false - positives is $0.2\times300=60$.

Step2: Calculate negative results for samples without organic matter

The number of samples without organic matter is $300$. The test gives a negative result for $80\%$ of samples without organic matter, so the number of true - negatives is $0.8\times300 = 240$.

Step3: Calculate negative results for samples with organic matter

The number of samples with organic matter is $700$. The test gives a negative result for $5\%$ of samples with organic matter, so the number of false - negatives is $0.05\times700=35$.

Step4: Calculate the probability that a positive result means the sample has organic matter

The total number of positive results is $665 + 60=725$. The probability $P$ that a sample has organic matter given a positive result is $\frac{665}{725}\approx0.917$. Rounding to one decimal place, $P\approx0.9$.

Answer:

The missing values in the table (from top - to - bottom, left - to - right) are: $60$, $35$. The probability that a soil sample contains organic matter given a positive result is $0.9$.