type the correct answer in each box. use numerals instead of words.\na new test is developed to test for…

type the correct answer in each box. use numerals instead of words.\na new test is developed to test for organic matter in soil samples, giving \positive\ or \negative\ results to indicate that a sample does or does not contain organic matter.\nfor 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.\na study included a population of 1,000 soil samples, and 70% of those studied where known to contain organic matter.\nfill in the missing values in the table and statement below. if necessary, round the percentage to one decimal place.\n| | number of samples | positive result | negative result |\n|--|--|--|--|\n| contains organic matter | 700 | 665 | |\n| does not contain organic matter | 300 | | 240 |\nif a soil sample test gives a positive result, it is % likely that the soil sample contains organic matter.\nreset next

type the correct answer in each box. use numerals instead of words.\na new test is developed to test for organic matter in soil samples, giving \positive\ or \negative\ results to indicate that a sample does or does not contain organic matter.\nfor 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.\na study included a population of 1,000 soil samples, and 70% of those studied where known to contain organic matter.\nfill in the missing values in the table and statement below. if necessary, round the percentage to one decimal place.\n| | number of samples | positive result | negative result |\n|--|--|--|--|\n| contains organic matter | 700 | 665 | |\n| does not contain organic matter | 300 | | 240 |\nif a soil sample test gives a positive result, it is % likely that the soil sample contains organic matter.\nreset next

Answer

Explanation:

Step1: Calculate false - negative samples

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

Step2: Calculate false - positive samples

The number of samples that do not contain organic matter is 300. The false - positive rate is 20%. So the number of false - positive samples is $300\times0.2=60$.

Step3: Calculate the total number of positive results

The number of true - positive results (samples with organic matter and positive test) is 665, and the number of false - positive results (samples without organic matter and positive test) is 60. So the total number of positive results is $665 + 60=725$.

Step4: Calculate the probability that a positive - result sample contains organic matter

The probability $P$ that a sample with a positive result contains organic matter is $\frac{665}{725}\times100%\approx91.7%$.

Answer:

Number of Samples Positive Result Negative Result
Contains Organic Matter 700 665 35
Does Not Contain Organic Matter 300 60 240
If a soil sample test gives a positive result, it is 91.7% likely that the soil sample contains organic matter.