The information for a particular area and radon testing is as follows ...

      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.