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The information for a particular area and radon testing is as follows: • 4 of 100...

The information for a particular area and radon testing is as follows:
• 4 of 100 homes have radon gas problems
• A test for radon gas is 85% accurate
• The test is performed in 10,000 homes in this area
a. Using the table below, create a matrix similar to the one in the Type I-Type II error notes.
1. Label the cells as true positives, false positives, false negatives, true negatives and Type I and Type II errors.
2. Complete the matrix to show the values for true positives, false positives (Type I), false negatives (Type II), and true negatives
3. Calculate the totals and add them to the matrix.
b. What is the chance that a positive radon test really means that there is radon in that house? Show this as a percentage with 3 decimal places.
c. Assume that the test results were negative for a particular house. What is the chance that there really is a radon problem in that house? Show this as a percentage with 3 decimal places.
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Answer #1
(a) Test
Positive Negative
Gas Problem Yes True Positive False Negative (Type II error)
No False Positive (Type I error) True Negative
Test
Positive Negative Total
Gas Problem Yes (85/100) * 400 = 340 400-340 = 60 (4/100) * 10000 = 400
No 9600 - 8160 = 1440 (85/100) *9600 = 8160 10000 - 400 = 9600
Total 1780 8220 10000
(b) Probability = 340/1780 = 0.19101 (19.101%)
(c) Probability = 60/8220 = 0.007299 (0.730%)
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