It has recently been discovered that a small number of people have a genetic mutation that gives them latent superpowers, known as the omega-gene. A laboratory test has been created to help identify people with the omega- gene, which returns either "positive" (indicating the subject has the omega-gene) or "negative" (indicating the subject does not have the omega-gene). The test returns a "true positive" result for 98% of people who do in fact have the omega-gene. However, the test also returns a "false positive" result for 6% of people who do not have the omega-gene. Anyone who is suspected of having the omega-gene must take the test exactly twice. (a) What is the probability that a person who does not have the omega-gene receives at least one negative result out of their two tests? 0.0199 因 (b) Many people on the island of Genosha have taken the test twice. It is discovered that 5% of these people received a positive result for both tests. Based on this information, what proportion of people from the island actually have the omega-gene?

It has recently been discovered that a small number of people have a genetic mutation that gives them latent superpowers, known as the omega-gene. A laboratory test has been created to help identify people with the omega- gene, which returns either "positive" (indicating the subject has the omega-gene) or "negative" (indicating the subject does not have the omega-gene). The test returns a "true positive" result for 98% of people who do in fact have the omega-gene. However, the test also returns a "false positive" result for 6% of people who do not have the omega-gene. Anyone who is suspected of having the omega-gene must take the test exactly twice. (a) What is the probability that a person who does not have the omega-gene receives at least one negative result out of their two tests? 0.0199 因 (b) Many people on the island of Genosha have taken the test twice. It is discovered that 5% of these people received a positive result for both tests. Based on this information, what proportion of people from the island actually have the omega-gene?

Name: It has recently been discovered that a small number of people have a
Uploaded: 2024-03-20T07:07:00.000Z
Channel: Bartleby
Description: It has recently been discovered that a small number of people have a genetic mutation that gives them latentsuperpowers, known as the omega-gene. A laboratory test has been created to help identify people with the omega-gene, which returns either "p

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

In 1991, researchers at the National Cancer Institute released the results of a study that investigated the effect of weed-killing herbicides on house pets. They examined 827 dogs from the homes where the herbicides was used on a regular basis, diagnosing the malignant lymphoma in 473 of them. Of the 130 dogs from the homes where no herbicides were used, only 19 were found to have lymphoma. Conduct a hypothesis test to determine whether the presence of the herbicide causes malignant lymphoma to form in dogs at a significance level of a = 0.01. State your conclusion.
Historically, the proportion of people who trade in their old car to a car dealer when purchasing a new car is 48%. Over the previous six months, in a sample of 115 new car buyers, 46 have traded in their old car. To determine whether the proportion of new car buyers that trade in their old car has this is sickly significantly decreased, what is the null and alternative hypothesis?
A researcher decides to conduct a study to observe the association between smoking cessation among long-term smokers and obesity since it has been previously well documented in the literature that smokers tend to gain weight when they stop smoking. The researcher notes that among the individuals who gain weight, many of them have developed heart problems or other medical problems that typically prevent them from exercising as much as their counterparts. In this case the individuals who developed these health problems had specific genetic markers putting them at higher risk of developing their health problems while they were smoking than their counterparts. This is an example of which of the following? Confounding Recall bias Statistical interaction Misclassification bias
The National Academy of Science reported that 41% of research in mathematics is published by US authors. The mathematics chairperson of a prestigious university wishes to test the claim that this percentage is no longer 41%. He has no indication of whether the percentage has increased or decreased since that time. He surveys a simple random sample of 186 recent articles published by reputable mathematics research journals and finds that 92 of these articles have US authors. Does this evidence support the mathematics chairperson’s claim that the percentage is no longer 41%? Use a 0.05 level of significance. Step 1 of 3: State the null and alternative hypotheses for the test. circle the answer below. H0 p=0.41 ha: p⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯0.41 A.<B.≠C.> Step 2 of 3: Compute the value of the test statistic. Round your answer to two decimal places Step 3 of 3: Draw a conclusion and interpret the decision. A. We reject the null hypothesis and conclude that there is insufficient evidence at a…
A low-level CDC bureaucrat wants to please his boss by gathering evidence that the current government mandated shut down of society is not causing people's mental health to deteriorate, so that it can safely be continued for several years if the expert says is necessary. He pulls a random sample of 1600 citizens, Gathering data on such items as income loss, weight gain, access to toilet paper, our spent binge watching Netflix, and number of injuries caused by household fight, and compiles all this into a significantly-weighted "misery index". The mean misery index from the sample is 99.2; it seems reasonable to use a population standard deviation o=19.1. A. Does this information provide significant evidence (at the 5% level) that the Nationwide mean misery index is less than 100? Set up appropriate null and alternative hypothesis, calculate the appropriate test statistic, find the p-value, and state your conclusion.
A study was conducted at the local skate park to determine how caffeine affected the performance of skateboarders during competitions. 100 skateboarders were selected from an upcoming competition roster. The researchers chose a random entry then proceeded to select every 4th entry until the desired sample size was reached.On the day of the competition, the sample was split (at random) into two groups. Each member of Group "A" was given a cup of decaf coffee while each member of Group "B" was given a cup of coffee containing 100mg of caffeine. (The skateboarders did not know which type of coffee they received.) As the competition progressed, the scores for each skateboarder were tracked.
The makers of a smartphone have received complaints that the face recognition tool often doesn't work, or takes multiple attempts to finally unlock the phone. They've upgraded to a new version and are claiming the tool has improved. To test the claim, a critic takes a random sample of 80 users of the new version (Group 1) and 75 users of the old version (Group 2). He finds that the face recognition tool works on the first try 70% of the time in the new version and 56% of the time in the old version. Can it be concluded that the new version is performing better? Test at α=0.10. Hypotheses: H0: p1 = p2 H1: p1 > p2 In this scenario, what is the p-value? Round to four decimal places. p-value=
In a study of chromosomal anomalies observed in a randomly selected sample of 1200 infertile men with either a zero or low sperm count, a team of researchers assigned the value of 1 for the presence of any chromosomal anomaly in the subject's sperm and the value of 0 for the absence of all chromosomal anomalies in the subject's sperm.Of the 600 men with zero sperm count, 48 had chromosomal anomalies. Of the 600 men with low sperm count, 15 had chromosomal anomalies. The researchers would like to test the hypothesesHo: P1 = P2Ha: P1 does not equal P2where p₁ the true proportion of all men with zero sperm count that have chromosomal anomalies and p₂ = the true proportion of all men with low sperm count that have chromosomal anomalies.What is the z standardized test statistic, for this test?
The National Institute of Mental Health published an article stating that in any one-year period, approximately 8.8% of American adults suffer from depression or a depressive illness. Suppose that in a survey of 2000 people in a certain city, 11.3% of them suffered from depression or a depressive illness. Conduct a hypothesis test to determine if the true proportion of people in that city suffering from depression or a depressive illness is more than the 8.8% in the general adult American population. Test the relevant hypotheses using a 5% level of significance. Give answer to at least 4 decimal places. a. What are the correct hypotheses? H0: H1: b.) Based on the hypotheses, find the following: c.) Test Statistic = d.) p-value = e.) Based on the above we choose to________________ f.) The correct summary would be:____________ that the true proportion of people in that city suffering from depression or a depressive illness is more than the percent in the general…
Although an increasing share of Americans are reading e-books on tablets and smartphones rather than dedicated e-readers, print books continue to be much more popular than books in digital format (digital format includes both e-books and audio books). A Pew Research Center survey of 1502 adults nationwide conducted January 8-February 7, 2019, found that 1081 of those surveyed had read a book in either print or digital format in the preceding 12 months. (You may regard the 1081 adults in the survey who had read a book in the preceding 12 months as a random sample of readers.) Andrew Perrin, "One-in-five Americans now listen to audiobooks," September 25, 2019 at www.pewresearch.org/fact-tank/2019/09/25/one-in-five-americans- now-listen-to-audiobooks/. The sampling scheme was more complex than an SRS, so the computation of the number in the sample who have read in the preceding 12 months and acting as if it were an SRS is oversimplified Macmillan Learning STATE: What can you say with 95%…
According to the CDC, as of MAY 2021, it is suspected that 2% of the US population currently have active coronavirus. According to Johns Hopkins, a particular type of COVID test (RT-PCR), has a false negative rate of 20%. That is, if a person has COVID, and takes this test, there is a 20% chance of testing negative. The false positive rate is about 5%. That means that about 5% of people who don't have COVID will nonetheless test positive. Consider the following two-way table for 10,000 randomly selected people who were tested for COVID using (RT-PCR). Positive test Negative test Total Has COVID A 40 200 No COVID 490 B 9800 Total 10000 1. fill in the missing values in the table. A • B • C • D 2. What is the probability of choosing someone who tested positive? 3. What is the probability of choosing someone who has COVID? 4. What is the probability of choosing someone who does not have COVID and tested positive? 5. What is the probability of choosing someone with COVID given that they…
Sickle-cell anemia is a hereditary chronic blood disease that is extremely severe when an individual carries two copies of the defective gene. It is particularly common in countries plagued by malaria, a parasiticinfection transmitted by mosquitoes. A study in Africa tested 543 children for the sickle-cell gene and also for malaria. In Group 1 which consisted of 136 children with the sickle-cell gene, 36 children had severe malariainfections. Group 2 consisted of 407 children without the sickle-cell gene, and 152 of them had severe malaria infections. Conduct a test to determine if the proportion of severe malaria infections among children withthe sickle-cell trait is different from that among children without. Test at 5% level of significance. Question: What is your p value and t statistic ?