Type I and Type II Errors
The information for a particular area and radon testing is as follows:
a. Using the table below, create a matrix similar to the one in the Type I-Type II error notes.
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.
|Gas Problem||Yes||True Positive||False Negative (Type II error)|
|No||False Positive (Type I error)||True Negative|
total actual radon = 10000* 3/100 = 300
|Gas Problem||Yes||(85/100) * 300 = 255||300-255 = 45||(3/100) * 10000 = 300|
|No||9700 - 8245 = 1455||(85/100) *9700 = 8245||10000 - 300 = 9700|
chance that a positive radon test really means that there is radon in that house
= P(yes for Gas problem| test is positive)
P(gas problem | negative test result)
= 0.543 %
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