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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 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.

Number of
Samples Positive
Result Negative
Result
Contains
Organic Matter 700 665
Does Not Contain
Organic Matter 300
240

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

Respuesta :

MrRoyal

Answer:

[tex]\begin{array}{cccc}{} & {Samples} & {Positive} & {Negative} & {Contains\ Organic\ Matter} & {700} & {665} & {[35 ]} & {Does\ not\ contain\ organic\ matter} & {300} & {[60]} & {240} \ \end{array}[/tex]

[tex]\% Pr= 95\%[/tex]

Step-by-step explanation:

Given

[tex]\begin{array}{cccc}{} & {Samples} & {Positive} & {Negative} & {Contains\ Organic\ Matter} & {700} & {665} & {[\ ]} & {Does\ not\ contain\ organic\ matter} & {300} & {[\ ]} & {240} \ \end{array}[/tex]

Solving (a): Complete the table

The sum of each row must equal to the samples.

i.e.

[tex]Positive + Negative = Samples[/tex]

For the samples that contain organic matter, we have:

[tex]665 + Negative = 700[/tex]

Collect like terms

[tex]Negative = 700 - 665[/tex]

[tex]Negative = 35[/tex]

For the samples that do not contain organic matter, we have:

[tex]Positive + 240 = 300[/tex]

Collect like terms

[tex]Positive = 300 -240[/tex]

[tex]Positive = 60[/tex]

So, the complete table is:

[tex]\begin{array}{cccc}{} & {Samples} & {Positive} & {Negative} & {Contains\ Organic\ Matter} & {700} & {665} & {[35 ]} & {Does\ not\ contain\ organic\ matter} & {300} & {[60]} & {240} \ \end{array}[/tex]

Solving (b): Proportion of samples that are positive if the sample contains organic matter

From the table, we have:

[tex]Samples = 700[/tex]

[tex]Contains\ Organic\ Matter\ n\ Positive = 665[/tex]

So, the percentage is:

[tex]\%Pr = \frac{Contains\ Organic\ Matter\ n\ Positive}{Samples} * 100\%[/tex]

[tex]\% Pr= \frac{665}{700} * 100\%[/tex]

[tex]\% Pr= \frac{665* 100}{700} \%[/tex]

[tex]\% Pr= \frac{66500}{700} \%[/tex]

[tex]\% Pr= 95\%[/tex]

Answer:

35, 60, 95%

Step-by-step explanation:

correct

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