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A 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.

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 were 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.

\begin{tabular}{|c|c|c|c|}
\hline
& \begin{tabular}{c}
Number of \\
Samples
\end{tabular} & \begin{tabular}{c}
Positive \\
Result
\end{tabular} & \begin{tabular}{c}
Negative \\
Result
\end{tabular} \\
\hline
\begin{tabular}{c}
Contains \\
Organic Matter
\end{tabular} & 700 & 665 & 35 \\
\hline
\begin{tabular}{l}
Does Not \\
Contain \\
Organic Matter
\end{tabular} & 300 & 60 & 240 \\
\hline
\end{tabular}

If a soil sample test gives a positive result, it is [tex]$\square$[/tex] \% likely that the soil sample contains organic matter.

Response:

Sagot :

GinnyAnswer
To fill in the missing values:

1. The number of samples that contain organic matter is given as 700.
2. Out of these 700 samples, the number of positive results (true positives) is 665, meaning there are 700 - 665 = 35 negative results (false negatives).
3. The number of samples that do not contain organic matter is 300.
4. For these 300 samples, the number of positive results (false positives) is 60, meaning there are 300 - 60 = 240 negative results (true negatives).
5. The probability that a positive result means the sample contains organic matter is 91.7%.

So the filled-in table and statement are:

[tex]\[ \begin{tabular}{|c|c|c|c|} \hline & \begin{tabular}{c} Number of \\ Samples \end{tabular} & \begin{tabular}{c} Positive \\ Result \end{tabular} & \begin{tabular}{c} Negative \\ Result \end{tabular} \\ \hline \begin{tabular}{c} Contains \\ Organic Matter \end{tabular} & 700 & 665 & 35 \\ \hline \begin{tabular}{l} Does Not \\ Contain \\ Organic Matter \end{tabular} & 300 & 60 & 240 \\ \hline \end{tabular} \][/tex]

If a soil sample test gives a positive result, it is 91.7% likely that the soil sample contains organic matter.
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