Question

# Type I and Type II Errors The information for a particular area and radon testing is...

Type I and Type II Errors

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

• 3 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.

 Test Positive Negative 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

 Test Positive Negative Total 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 Total 1710 8290 10000
 Test Positive Negative Total Gas Problem Yes 255 45 300 No 1455 8245 9700 Total 1710 8290 10000

b)

chance that a positive radon test really means that there is radon in that house

= P(yes for Gas problem| test is positive)

= 255/1710

= 0.14912

= 14.912%

c)

P(gas problem | negative test result)

= 45/8290

= 0.005428

= 0.543 %

#### Earn Coins

Coins can be redeemed for fabulous gifts.