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A new test is developed to detect a certain allergy, giving "positive" or "negative" results to indicate whether a person has the allergy.

- For a person who has the allergy, the test will give a positive result 82% of the time and a negative result (false negative) 18% of the time.
- For a person who does not have the allergy, the test will give a positive result (false positive) 10% of the time and a negative result 90% of the time.

A study included a population of 10,000 people, and 1% of those studied were known to have the allergy.

Fill in the missing values in the table below and complete the statements that follow. Round the percentages to the nearest tenth, if necessary.

[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline & \text{Number of People} & \text{Positive Test} & \text{Negative Test} \\
\hline \text{Have Allergy} & 100 & \square & 18 \\
\hline \text{Don't Have Allergy} & 9900 & 990 & \square \\
\hline
\end{tabular}
\][/tex]

If an individual's test gives a positive result, it is \square\% likely that the person has the allergy.

Therefore, this test \square (should/should not) be used for allergy testing.

Sagot :

GinnyAnswer
Sure, let's fill in the missing values and complete the statements step-by-step based on the given information and numerical results.

1. The number of people with the allergy is given as 100.
2. The number of positive test results for those with the allergy is 82.
3. The number of negative test results for those with the allergy is 18.
4. The number of people without the allergy is 9900.
5. The number of positive test results for those without the allergy is 990.
6. The number of negative test results for those without the allergy is 8910.
7. The positive predictive value (PPV) or the likelihood that a person has the allergy if the test is positive is 7.6%.
8. The test should not be used for allergy testing.

Now, let's complete the table and the statements:

\begin{tabular}{|c|c|c|c|}
\hline & \begin{tabular}{c}
Number of \\
People
\end{tabular} & Positive Test & Negative Test \\
\hline Have Allergy & 100 & 82 & 18 \\
\hline Don't Have Allergy & 9900 & 990 & 8910 \\
\hline
\end{tabular}

Complete the statements:

If an individual's test gives a positive result, it is 7.6\% likely that the person has the allergy.

Therefore, this test should not be used for allergy testing.
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