The metal detector at the entrance of a courthouse is used to detect the presence of a weapon when someone enters the building. The metal detector should only sound, indicating a positive test result, when a weapon is present. A metal detector should remain silent, indicating a negative test result, when a weapon is not present.

1. Classify each of the following scenarios as a true positive, false positive, true negative, or false negative. (4 x 2 pt = 8 pt)
2. A person walks through the metal detector and an alarm sounds. This person did not have a weapon.

False negative

3. A person walks through the metal detector and the alarm did not sound. The person did not have a weapon.

True negative

4. A person walks through the metal detector and an alarm sounds. A weapon was found on the person.

True positive

5. A person walks through the metal detector and the alarm did not sound. A weapon was found on the person.

False positive

A security team is setting up a new walk-through metal detector and decided to run some tests on the current calibration of the machine. Members of the team walk through carrying metallic items of different sizes. Some items are weapons which should cause the alarm to sound. Other items are harmless, like jewelry or coins, which should not cause the alarm to sound. The following table shows the results of their test.

	Weapon	Harmless Item	Totals
Positive (alarm sounds)	True Positive 149	False Positive 311	460
Negative (no alarm)	False Negative 14	True Negative 91	105
Totals	163	402	565

Answer as a percentage rounded to two decimal places. Show your calculations.

1. What is the probability of a positive test result from the metal detector? (4 pts)

2. What is the probability of a positive test result from the metal detector given that a weapon is present? This is the sensitivity of the metal detector. (4 pts)

3. What is the probability of a negative test result from the metal detector given that a weapon was present? This is the false negative rate of the metal detector. (4 pts)

4. What is the probability of a negative test result from the metal detector given that a harmless item was present? This is the specificity of the metal detector. (4 pts)

5. What is the probability of a positive test result from the metal detector given that a harmless item was present? This is the false positive rate of the metal detector. (4 pts)

With the current settings the metal detector was able to find most metal objects regardless of type. With such a high sensitivity this would cause many follow up searches which increase the amount of time someone would need to spend to go through the security check. Using all the same items as before, more tests were conducted with lower sensitivity.

1. The following table shows the results of their testing, but it is not complete yet. Copy your answers from p. 2 (p. 258 in packet) questions 3, 4, 5, and 6, into the correspondingly numbered cells in the top row of the table. (1 pt)

Sensitivity	False Negative Rate	Specificity	False Positive Rate
3.		4.		5.		6.
86.00%	14.00%	33.75%	66.25%
76.00%	24.00%	47.50%	52.50%
62.00%	38.00%	62.50%	37.50%

Answer the following questions in complete sentences. Mention specific column names and/or values to support your conclusions.

1. As the sensitivity of the metal detector decreases, does it become more likely or less likely that the machine will not sound an alarm when a weapon is present? Explain. (3 pts)

2. As the sensitivityof the metal detector decreases, does the specificity of the metal detector increase or decrease? Explain. (2 pts)

3. As the sensitivity of the metal detector decreases, does it become more likely or less likely that the machine will sound an alarm when a weapon is not present? Explain. (3 pts)