Suppose you were selected from a population at random to take a medical test. It is believed that there is a 5% chance that you are ill (i.e. you have the disease), since that is the disease prevalence for asymptomatic people like yourself. Suppose that the test you take has some error rate. If you are ill, it will correctly identify you as positive 90% of the time. If you not ill, it will give a false positive 2% of the time. What is probability that you are ill given a positive test result?

Suppose you were selected from a population at random to take a medical test. It is believed that there is a 5% chance that you are ill (i.e. you have the disease), since that is the disease prevalence for asymptomatic people like yourself. Suppose that the test you take has some error rate. If you are ill, it will correctly identify you as positive 90% of the time. If you not ill, it will give a false positive 2% of the time. What is probability that you are ill given a positive test result?

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...

See similar textbooks

Similar questions

On Wikipedia it said the proportion of people who bite their nails is over 31%. You aren't sure if you can believe Wikipedia, so you randomly sample 209 people and find 83 of them bite their nails. The hypothesis test with α=0.05 had a p-value of 0.0033, which causes you to reject the null, and believe that Wikipedia was right. Assuming the true proportion really was 0.31, if another sample of 209 people was taken, what is the probability of getting a proportion as high as 83/209 or higher?
Suppose that 6% of a particular population have a particularly nasty disease. There is a test for the disease that correctly identifies those with the disease 98% of the time. However, the same test gives a false positive 1% of the time. Suppose that a random person from this population is given the test as part of a wellness exam. Give answers in decimal form rounded to 4 decimal places as needed. A. Suppose that a random person comes in for a wellness exam and tests positive for the disease. What is the probability that she actually has the disease? B. Suppose that a person comes in for a wellness exam and tests negative. What is the probability that this person does not have the disease? C. What proportion of the total population will test positive? D. What proportion of the total population will not have the disease and will test negative?
A poll reports that 47% of Canadians download movies on their computers.The poll has a margin of error of 4.8%, 19 times out of 20.Choose the statement that best explains what this means. Question 6 options: If you had taken another poll, there is a 95% chance that somewhere between 51.8% and 42.2% of people polled would download movies. If you had taken another poll, there is a 90% chance that somewhere between 51.8% and 42.2% of people polled would download movies. If you had taken another poll, there is a 19% chance that somewhere between 49.4% and 44.6% of people polled would download movies. If you had taken another poll, there is a 95% chance that somewhere between 49.4% and 44.6% of people polled would download movies.
An anger-management course claims that, after completing its seminar, participants will lose their tempers less often. Always a skeptic, you decide to test this claim. A random sample of 12 seminar participants is chosen, and these participants are asked to record the number of times that they lost their tempers in the two weeks prior to the course. After the course is over, the same participants are asked to record the number of times that they lost their tempers in the next two weeks. The following table lists the results of the survey. Using these data, test the claim at the 0.01 level of significance assuming that the population distribution of the paired differences is approximately normal. Let participants before completing the anger-management course be Population 1 and let participants after completing the anger-management course be Population 2. Number of Times Temper Was Lost during a Two-Week Period Before 10 6 8 10 6 3 10 3 8 After 6 7 4 4 8 6 4 9 3 7 Copy Data Step 2 of 3:…
You are testing the difference between high school freshmen and seniors on SAT performance. The null hypothesis is that the population mean SAT score of the seniors is equal to the population mean SAT score of the freshmen. You randomly sample 20 students in each grade and have them take the SAT. You find that the sample mean of the seniors is significantly higher than the sample mean of the freshmen. Which alternative hypothesis is accepted? The population mean SAT score of the seniors is less than the population mean SAT score of the freshmen. The population mean SAT score of the seniors is greater than the population mean SAT score of the freshmen. You cannot be sure which alternative hypothesis to accept. You just know that the null hypothesis was rejected
Predict whether they are cause-effect, accidental, or common-cause. Explain your conclusion and, if they are cause-effect, explain which causes the other and why. "People who drink more coffee in the morning are more likely to have insomnia (the inability to sleep) at night."