The probability that an individual randomly selected from a particular population has a certain disease is 0.06. A diagnostic test correctly detects the presence of the disease 93% of the time andcorrectly detects the absence of the disease 98% of the time. If the test is applied twice, the two test results are independent, and both are positive, what is the (posterior) probability that theselected individual has the disease? [Hint: Tree diagram with first-generation branches corresponding to Disease and No Disease, and second- and third-generation branches corresponding toresults of the two tests.]

Given probability that an individual randomly selected from a particular population has a certain…

Answered: correctly detects the absence of the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A study is conducted in a large high school to determine if the proportion of students who plan to come to the upcoming football game differs across the grades. A random sample of 50 ninth graders, 50 tenth graders, 50 eleventh graders, and 50 twelfth graders was selected. The responses are displayed in the table. The principal would like to know if these data provide convincing evidence that the distribution of responses differs across the grades in the population of all students in her school. The random and 10% conditions are met, and this table of expected counts shows that all expected counts are at least 5. What is the value of the chi-square test statistic for this test? χ‑2 = 0.49 χ‑2 = 0.70 χ‑2 = 0.84 χ‑2 = 200
Suppose there are 115 patients in a clinical trial. Of those, 35 received a real medication and were cured of their illness, 20 received the real drug and were not cured, 28 received a sugar pill (placebo) and were not cured and the remaining received a sugar pill and were cured. When testing (at the 5% level of significance) whether the medication was effective (or thinking about it another way, testing whether getting the medication and being cured is independent or not), what is the critical value (please round your answer to 3 decimal nlaces)
for a given level of the probability of rejecting the null hypothesis when its true, if we want to decrease the probability of not rejecting null hypothesis when it is false the sample must A) decrease B) remain the same C) increase D) increase or decrease since it has no impact on probability of not rejecting null hypothesis when it’s false
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The table below provides another look at the data presented in item 1. This table includes a third variable, stone size, making a three-way table (i.e. two 2 X 2 tables). ô อิ = 1 Stones size Small = kidney stones. Find and 1 2 Large 1 Outcome Success Failure Success Failure Let represent the odds ratio for the 2 X 2 table for small kidney stones, and let represent the odds ratio for the 2 X 2 table for large Round your answers to 2 places after the decimal. Treatment A 81 6 2 192 71 Treatment B 234 36 55 25 2
You currently work for the DARPA, the Defense Advanced Research Projects Agency. You've received reports of some strange things occurring in the small town of Hawkins, Indiana. Let U be a random variable equal to 1 if the citizen has been to the Upside Down and 0 otherwise. Let S be a random variable equal to 1 if a citizen reports being in the presence of a group of misfit kids who claim to be "saving the town" and 0 otherwise The table below shows the joint probability density function for the galactic population Share of Population 0.15 0.32 0.50 0.03 U 0 0 1 1 S 1 0 1 0 Round to 2 decimal places where necessary, unless otherwise stated. Leave your answer in decimals, rather than convert to percentages. A. Evaluate Fu,s (1,0): B. Calculate the share of people who have been to the Upside Down in the population. That is, E(U): C. Calculate the probability of having gone to the Upside Down conditional on meeting this band of misfit kids?. That is, Fus (11):
You are hiking through the woods, and come across some tracks; based on your expe- rience, you estimate there is a 40% chance the tracks are from a dog, a 30% chance the tracks are from a wolf, a 20% chance the tracks are from a coyote, and a 10% chance the tracks are from some other animal. Your friend, also a nature lover, notices some white hairs in the tracks. They know that 20% of dogs have white hair, 50% of wolves have white hair, 10% of coyotes have white hair, and 30% of other animals in the area have white hair. What are the odds of these tracks coming from a dog, wolf, coyote, or other animal?

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