not cause the alarm to sound. The following table shows the results of their test. Part...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
not cause the alarm to sound. The following table shows the results of their test. Part 1: Metal Detectors 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. Totals (a) Positive (alarm sounds) Weapon True Positive Harmless Item False Positive 133 271 False Negative True Negative Negative (no alarm) 8 104 141 375 Totals 404 112 516 (4 x 2 pt = 8 pt) Answer as a percentage rounded to two decimal places. Show your calculations. a. A person walks through the metal detector and the alarm did not sound. The person did not have a weapon. 2. What is the probability of a positive test result from the metal detector? (4 pts) b. A person walks through the metal detector and the alarm did not sound. A weapon was found on the person. 3. 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) C. A person walks through the metal detector and an alarm sounds. This person did not have a weapon. 4. 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) d. A person walks through the metal detector and an alarm sounds. A weapon was found on the person. 5. 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) 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. Note that the metal detector can only look for the presence of metal and cannot discern if the metal item is a weapon or not. 7. The following table shows the results of their testing, but it is not complete yet. Copy your answers from p. 2 questions 3, 4, 5, and 6, into the correspondingly numbered cells in the bottom row of the table. 6. 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) 3. (1 pt) Sensitivity False Negative Rate Specificity False Positive Rate 62.00% 38.00% 62.50% 37.50% 76.00% 24.00% 47.50% 52.50% 86.00% 14.00% 33.75% 66.25% 4. 5. 6. Answer the following questions in complete sentences. 8. As the Sensitivity of the metal detector increases, what happens to the False Negative Rate? In context of the metal detector, explain what this means in practice? (3 pts) Part 2: Disease Detection Suppose a new rapid screening test is being developed to detect a disease. Patients who take the new test also take an older test to confirm the results. The older test is 100% accurate, but since it is slower and more invasive, it is not a good choice for testing the general population. It is estimated that the new test has a sensitivity of 97% and a specificity of 95%. 11. Consider a population of 50,000 patients where a (b) 9% disease prevalence is assumed. Fill in the missing numbers in the breakdown below based on the use of the new test. Show your work. (6 x 2 pt = 12 pt) a. Number of Infected People 9% of Population Population 50,000 b. Number of Healthy People (d). 91 % of Population 9. As the Sensitivity of the metal detector increases, what happens to the Specificity? In context of the metal detector, explain what this means in practice? (3 pts) c. Number of Positive Test Results (97% of Infected Get a Positive Result) d. Number of Negative Test Results (3% of Infected Get a Negative Result) e. Number of Positive Test Results (5% of Healthy Get a Positive Result) f. Number of Negative Test Results (95% of Healthy Get a Negative Result) True Positives (TP) False Negatives (FN) False Positives (FP) True Negatives (TN) 10. As the Sensitivity of the metal detector increases, what happens to the False Positive Rate? In context of the metal detector, explain what this means in practice? 12. Fill in the table based on the results in problem 11 above. Has Disease (Infected) (8 pts) Does Not Have Disease (Healthy) Totals (3 pts) Test Positive Test Negative Totals 50,000 not cause the alarm to sound. The following table shows the results of their test. Part 1: Metal Detectors 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. Totals (a) Positive (alarm sounds) Weapon True Positive Harmless Item False Positive 133 271 False Negative True Negative Negative (no alarm) 8 104 141 375 Totals 404 112 516 (4 x 2 pt = 8 pt) Answer as a percentage rounded to two decimal places. Show your calculations. a. A person walks through the metal detector and the alarm did not sound. The person did not have a weapon. 2. What is the probability of a positive test result from the metal detector? (4 pts) b. A person walks through the metal detector and the alarm did not sound. A weapon was found on the person. 3. 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) C. A person walks through the metal detector and an alarm sounds. This person did not have a weapon. 4. 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) d. A person walks through the metal detector and an alarm sounds. A weapon was found on the person. 5. 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) 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. Note that the metal detector can only look for the presence of metal and cannot discern if the metal item is a weapon or not. 7. The following table shows the results of their testing, but it is not complete yet. Copy your answers from p. 2 questions 3, 4, 5, and 6, into the correspondingly numbered cells in the bottom row of the table. 6. 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) 3. (1 pt) Sensitivity False Negative Rate Specificity False Positive Rate 62.00% 38.00% 62.50% 37.50% 76.00% 24.00% 47.50% 52.50% 86.00% 14.00% 33.75% 66.25% 4. 5. 6. Answer the following questions in complete sentences. 8. As the Sensitivity of the metal detector increases, what happens to the False Negative Rate? In context of the metal detector, explain what this means in practice? (3 pts) Part 2: Disease Detection Suppose a new rapid screening test is being developed to detect a disease. Patients who take the new test also take an older test to confirm the results. The older test is 100% accurate, but since it is slower and more invasive, it is not a good choice for testing the general population. It is estimated that the new test has a sensitivity of 97% and a specificity of 95%. 11. Consider a population of 50,000 patients where a (b) 9% disease prevalence is assumed. Fill in the missing numbers in the breakdown below based on the use of the new test. Show your work. (6 x 2 pt = 12 pt) a. Number of Infected People 9% of Population Population 50,000 b. Number of Healthy People (d). 91 % of Population 9. As the Sensitivity of the metal detector increases, what happens to the Specificity? In context of the metal detector, explain what this means in practice? (3 pts) c. Number of Positive Test Results (97% of Infected Get a Positive Result) d. Number of Negative Test Results (3% of Infected Get a Negative Result) e. Number of Positive Test Results (5% of Healthy Get a Positive Result) f. Number of Negative Test Results (95% of Healthy Get a Negative Result) True Positives (TP) False Negatives (FN) False Positives (FP) True Negatives (TN) 10. As the Sensitivity of the metal detector increases, what happens to the False Positive Rate? In context of the metal detector, explain what this means in practice? 12. Fill in the table based on the results in problem 11 above. Has Disease (Infected) (8 pts) Does Not Have Disease (Healthy) Totals (3 pts) Test Positive Test Negative Totals 50,000
Expert Answer:
Posted Date:
Students also viewed these mathematics questions
-
Find the slopes of the curves at the given points. Sketch the curves along with their tangents at these points. r = sin 2; = /4, 3/4
-
Because ADRs are denominated in dollars and are traded in the United States, they present less foreign exchange risk to U.S. investors than do the underlying foreign shares of stock. Comment.
-
At the CERN particle accelerator in Geneva, Switzerland, protons are accelerated to a speed of 0.999999972c. In the tunnel next to the beam line a worker drops a wrench from a height of 1.1 m above...
-
Identify whether each of the following headlines represents a microeconomic topic or a macroeconomic topic. a. U.S. Unemployment Rate Reaches Historic Highs b. General Motors Closes Auto Plant in...
-
In your presentation to a venture capital company, you are pitching your research plan for a smartphone application that does short-term cash flow forecasts. Describe how you would use each type of...
-
QUESTION 2 OF 7 Choose food product that is not a listed allergen: Choose only ONE best answer. A Pecan Nut B Coconut C Cashew Nut D Pistachio CON
-
Miss Bajadu is one of your cherished customers who has maintained a satisfactory account for the past 12 years. She has been promoted and wants to relocate to an area that befits her current status....
-
How do hormones modulate immune function and inflammatory responses, and what are the implications of hormone-immune interactions for autoimmune diseases, allergic reactions, and host-pathogen...
-
Cash sales are 4 0 percent in a given monin, with the remainder going into accounts receivable. All receivables are cotected in the monin tollowing tne sale, Esquire sells all or its goods for $ 2...
-
Diana replied, "I agree that there are more problems to deal with than just parking, Tony. But if none of us can talk to one another, we can't deal with THIS problem, let alone others. This...
-
TKD Inc. started the year with $590,000 in beginning inventory. During the year, TKD Inc. purchased an additional $800,000 in inventory. At the end of the year, TKD Inc. employees performed a...
-
discuss the emerging role of hormone-based therapies, such as hormone replacement therapy (HRT) and hormone-targeted cancer treatments, in managing hormone-related disorders and optimizing patient...
-
32- A certain amplifier has an output voltage of 8.4 V p-p at the midland frequency range. The output at the critical frequency is equal to---------------. Choose one of the options: a. 4.2 Vrms b....
-
The time to assemble the first unit on a production line is 10 hours. The learning rate is 0.94. Approximately how long will it take for the seventh unit to be assembled? The number of hours needed...
Study smarter with the SolutionInn App