Medical tests sometimes produce incorrect results. When a test is designed to determine whether a patient has a certain disease, a false positive result indicates that a patient has the disease when the patient does not have it. A false negative result indicated that a patient does not have the disease when the patient does have it. Consider a large-scale medical test that screens for a disease where there were 5 cases in 1000 people of the population. It is known that the test has a false positive rate of 3% and a false negative rate of 1%. (a) What is the probability that a randomly chosen person who tests positive for the disease actually has the disease? (b) What is the probability that a randomly chosen person who tests negative for the disease does not indeed have the disease?

Medical tests sometimes produce incorrect results. When a test is designed to determine whether a patient has a certain disease, a false positive result indicates that a patient has the disease when the patient does not have it. A false negative result indicated that a patient does not have the disease when the patient does have it. Consider a large-scale medical test that screens for a disease where there were 5 cases in 1000 people of the population. It is known that the test has a false positive rate of 3% and a false negative rate of 1%. (a) What is the probability that a randomly chosen person who tests positive for the disease actually has the disease? (b) What is the probability that a randomly chosen person who tests negative for the disease does not indeed have the disease?

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

The blue catfish (Ictalurus Furcatus) is the largest species of North Amercian catfish. The current world record stands at 143 pounds, which was caught in the John H. Kerr Reservoir (Bugg's Island Lake) located in Virginia. According to Amercian Expedition, the average weight of a blue catfish is between 20 to 40 pounds. Given that the largest blue catfish ever caught was at the John H. Kerr Reservoir, you believe that the mean weight of the fish in this reservoir is greater than 40 pounds. If you are going to test this claim, what would be your null and alternative hypotheses? Ho: HA: p> v Submit Question
Please help me with the following sections: d, e, f, g, h and i Thank you!
Suppose the prevalence of "dance fever" at a college is 40% among women and 10% among men. If there are half as many men as women, what is the overall prevalence of dance fever at the college? What proportion of people without dance fever at that college are women?
8 students took a test. 3 of them scored 4, 4 and 7 marks respectively. Given that the median and mode is 5, the upper quartile is 8 and the largest score is thrice the smallest score, find the scores of the other 5 students.
Please also explain why you determined whether or not the results are statistically significant. In another memory experiment, the mean scores for participants in Condition A and Condition B came out exactly the same!
The claim is that the proportion of peas with yellow pods is equal to 0.25 (or 25%). The sample statistics from one experiment include 450 peas with 117 of them having yellow pods. Find the value of the test statistic.
The blue catfish (Ictalurus Furcatus) is the largest species of North Amercian catfish. The current world record stands at 143 pounds, which was caught in the John H. Kerr Reservoir (Bugg's Island Lake) located in Virginia. According to Amercian Expedition, the average weight of a blue catfish is between 20 to 40 pounds. Given that the largest blue catfish ever caught was at the John H. Kerr Reservoir, you believe that the mean weight of the fish in this reservoir is greater than 40 pounds. Use the data below, which represents the summary statistics for 48 blue catfish caught at this reservoir, and a 0.05 significance level to test the claim that the mean weight of the fish in the John H. Kerr Reservoir is greater than 40 pounds. n = 48; ī = 40.77 pounds; s = 5.04 pounds a) Identify the null and alternative hypotheses? Но: ? H1: ? b) What type of hypothesis test should you conduct (left-, right-, or two-tailed)? O left-tailed O right-tailed O two-tailed c) Identify the appropriate…
The results of a recent study show that the proportion of people in the western United States who use seat belts when riding in a car or truckis under 84%. You want to support this claim.
A student pursuing a degree in English as a second language believes the proportion female factory workers who can't speak English is less than the proportion of male factory workers who can't speak English. To test her claim she randomly selects 373 female factory workers and out of them 43 could not speak English. She then randomly selects 215 male factory workers and out of them 65 could not speak English. Test her claim at .=0.05 to see if she was right. The correct hypotheses are: H : PF Pu (claim) H : PF 2 PM HA: PF < Pr (claim) H : PF = PM HA: PF + PM (claim) Since the level of signficance s0.05 the critical value is-1.64s The test statistic is pound to 3 places) The pvalue is round to 3 places) The decision can be made to oreject H, odo not reject í, The final conclusion is that: There is enough evidence to reject the claim that the proportion female factory workers who can't speak English is less than the proportion of male factory workers who can't speak English. There is…