Composite Sampling for Diabetes Currently, the rate for new cases of diabetes in a year is 3.4 per 1000 (based on data from the Centers for Disease Control and Prevention). When testing for the presence of diabetes, the Portland Diagnostics Laboratory saves money by combining blood samples for tests. The combined sample tests positive if at least one person has diabetes. If the combined sample tests positive, then the individual blood tests are performed. In a test for diabetes, blood samples from 10 randomly selected subjects are combined. Find the probability that the combined sample tests positive with at least 1 of the 10 people having diabetes. Is it likely that such combined samples test positive?

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Asked Jan 23, 2020
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Composite Sampling for Diabetes Currently, the rate for new cases of diabetes in a year is 3.4 per 1000 (based on data from the Centers for Disease Control and Prevention). When testing for the presence of diabetes, the Portland Diagnostics Laboratory saves money by combining blood samples for tests. The combined sample tests positive if at least one person has diabetes. If the combined sample tests positive, then the individual blood tests are performed. In a test for diabetes, blood samples from 10 randomly selected subjects are combined. Find the probability that the combined sample tests positive with at least 1 of the 10 people having diabetes. Is it likely that such combined samples test positive?

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Expert Answer

Step 1

Here, new case of diabetes rate is 3.4 per 1000 and there are ten people having diabetes then the diabetes rate is considered as independent.

Step 2

Also, the probability that people did not have diabetes rate is,

Statistics homework question answer, step 2, image 1
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Step 3

So, one event of getting people did not have diabetes in second selection is not affected by another event of getting people did not have diabetes in first selection.

Similarly, the ‘event of getting a people did not have diabetes in tenth selection’ is not affected by...

Statistics homework question answer, step 3, image 1
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