A screening test for cancer has a low false positive rate and a low false negative rate, in that,with careful use, one finds the disease in 95% of the patients having it, and only 5% of thepatients not having it. Assume that 4% of a certain population has the disease. What is a theprobability that a person who reacts positively to the test will, in fact, have the disease?

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Answered: probability that a person who reacts…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Alpha Inflation, which happens when doing multiple t-tests, refers to increasing the probability of getting a ______ result. False Positive Insignificant False Negative Statistically Significant
A man claims to have extrasensory perception (ESP). As a test, a fair coin is flipped 29 times, and the man is asked to predict the outcome in advance. He gets 25 out of 29 correct. What is the probability that he would have done at least this well if he had no ESP?Probability =
A man claims to have extrasensory perception (ESP). As a test, a fair coin is flipped 20 times, and the man is asked to predict the outcome in advance. He gets 18 out of 20 correct. What is the probability that he would have done at least this well if he had no ESP? Probability =
Hepatic Disease Suppose we observe 84 alcoholics with cirrhosis of the liver, of whom 29 have hepatomas-that is, liver-cell carci- noma. Suppose we know, based on a large sample, that the risk of hepatoma among alcoholics without cirrhosis of the liver is 24%. 5.50 What is the probability that we observe exactly 29 alcoholics with cirrhosis of the liver who have hepatomas if the true rate of hepatoma among alcoholics (with or without cirrhosis of the liver) is .24?
Computing the probability of the event "drawing a second red ball from a bag of colored balls after having kept the red ball that was drawn first from the bag" is an example of
Medical researchers have developed a test for a PKP2 gene mutation in humans (which significantly increases cardiac health risks. 1% of the population has this mutation. The test is 95% accurate le a 5% false negative rate and a 5% false positive rate What is the probability that a person has the mutation given that they tested positive? HINT use Bayes Theorem O AIN 0 61% 0.1% 0 14%
Hypertension A national study found that treating people appropriately for high blood pressure reduced their overall mortality by 20%. Treating people adequately for hypertension has been difficult because it is estimated that 50% of hypertensives do not know they have high blood pressure, 50% of those who do know are inadequately treated by their physicians, and 50% who are appropriately treated fail to follow this treatment by taking the right number of pills. USE SALT (a) What is the probability that among 10 true hypertensives at least 50% are being treated appropriately and are complying with this treatment? (Round your answer to four decimal places.) (b) What is the probability that at least 8 of the 10 hypertensives know they have high blood pressure? (Round your answer to four decimal places.) (c) If the preceding 50% rates were each reduced to 35% by a massive education program, then what effect would this change have on the overall mortality rate among true hypertensives;…
Sleepwalking Assume that 29.2% of people have sleepwalked (based on “Prevalence and Comorbidity of Nocturnal Wandering in the U.S. Adult General Population,” by Ohayon et al., Neurology, Vol. 78, No. 20). Assume that in a random sample of 1480 adults, 455 have sleepwalked. a. Assuming that the rate of 29.2% is correct, find the probability that 455 or more of the 1480 adults have sleepwalked. b. Is that result of 455 or more significantly high? c. What does the result suggest about the rate of 29.2%?
Test for TB TB absent TB present Negative 1739 8 Positive 51 22 Data for TB testing using X-ray imaging Table shows the results of using X-ray imaging as a diagnostic test for tuberculosis in patients with known TB status. Use it to answer the questions below. 1. Calculate the marginal probabilities of the individual random variables, i.e. the probability of positive and negative X-ray test results, and of TB being present and absent. 2. Find the probability of positive result given that TB is absent (false positive rate) and the probability of a negative result given that TB is absent (specificity). 3. Find the probability of negative result given that TB is present (false negative rate) and the probability of a positive result given that TB is present (sensitivity). 4. Find the probability that a person who tests positive actually has TB (probability of TB present given a positive result). 5. Find the probability that a person who tests negative does not have TB (probability of no TB…

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