Polymerase chain reaction (PCR) is a method widely used to diagnose COVID-19 infections. Suppose that if a person does not have COVID-19, the test will be negative 84% of the time, and be positive 16% of the time; if the person does have COVID-19, the test will be positive 88% of the time, and be negative 12% of the time. Melbourne has a population of 5 million. Suppose that on the 15th of January 2021, there were 50 actual COVID-19 infections in Melbourne. A randomly selected person who lives in Melbourne is given a PCR test. This PCR test is positive. Without any other information about this person, what is the probability that this person has COVID-19? Suppose that on the 15th of January 2022, there were 300,000 actual COVID-19 infections in Melbourne. A randomly selected person who lives in Melbourne is given a PCR test. This PCR test is positive. Without any other information about this person, what is the probability that this person has COVID-19? Based on your answers above, explain why it is important to take the base rate into account when drawing conclusions from the test?

Polymerase chain reaction (PCR) is a method widely used to diagnose COVID-19 infections. Suppose that if a person does not have COVID-19, the test will be negative 84% of the time, and be positive 16% of the time; if the person does have COVID-19, the test will be positive 88% of the time, and be negative 12% of the time. Melbourne has a population of 5 million. Suppose that on the 15th of January 2021, there were 50 actual COVID-19 infections in Melbourne. A randomly selected person who lives in Melbourne is given a PCR test. This PCR test is positive. Without any other information about this person, what is the probability that this person has COVID-19? Suppose that on the 15th of January 2022, there were 300,000 actual COVID-19 infections in Melbourne. A randomly selected person who lives in Melbourne is given a PCR test. This PCR test is positive. Without any other information about this person, what is the probability that this person has COVID-19? Based on your answers above, explain why it is important to take the base rate into account when drawing conclusions from the test?

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 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?
A human factors psychologist is interested in how alcohol impacts driving performance. A sample of participants was randomly assigned into one of three different conditions of alcohol blood levels (abl). The participants then operate a driving simulator and each participant was measured on how much time (in seconds) they spent on a target when steering. The more time they spend on a target, the better their driving skills. What can the psychologist conclude with an α of 0.01? abl 1 abl 2 abl 3 221192171247234281238171 180146178134200170208156 180132172137154154176178 A) Obtain/compute the appropriate values to make a decision about H0.critical value = ; test statistic = Decision: B) Compute the corresponding effect size(s) and indicate magnitude(s).η2 = Magnitude= C) Conduct Tukey's Post Hoc Test for the following comparisons:2 vs. 3: difference = 1 vs. 3: difference = Conduct Scheffe's Post Hoc Test for the following comparisons:1 vs. 3: test statistic = 1…
The next two questions go together. You cross true-breeding lines of tall, purple-flowered pea plants with short, white-flowered pea plants and find that all the F₁ offspring are tall and purple-flowered. When an F₁ is self-pollinated, you get 109 tall, purple: 19 tall, white: 22 short, purple: 10 short, white plants. Your null hypothesis is that the offspring fit a model of two independently-assorting loci, with tall dominant to short and purple dominant to white, and that deviations from the 9:3:3:1 ratio are due to chance. Fill out the table to calculate the x2 value for the data. For the last column, where decimals are involved, write your answer to one decimal point (e.g. 5.2). Phenotype Observed Expected o-e (o-e)² Tall, purple (o-e)²/e 109 Tall, white 19 Short, 22 purple Short, 10 white Total 160 160 How many degrees of freedom are there? [Select] What is the appropriate critical value of the x2 statistic at p=0.05? [Select] What is the p-value range (for example 0.5-0.1 or…
Can someone explain to me what I may have done wrong on this question? A national newspaper reported that 10% of Americans have received the vaccine for Covid-19 (as of February 10, 2021). A local community is concerned that their citizens are not being vaccinated at the same rate as the rest of the nation. In a random sample of 150 residents of this community, 8% have received the vaccine. Is there significant evidence that this community’s rate of vaccination is lower than the nation’s? Test an appropriate hypothesis and state your conclusion. (Make sure to check any necessary conditions and to state a conclusion in the context of the problem.) Ho: p = .1 Ha: p < .1 p-hat (sample proportion) = 0.08, n = 150 n*p-hat = 150*0.08 = 12 and n(1-p-hat) = 150*0.92 = 138 sample is random, sample size is less than 10 percent of the population 0.08-0.1/sqrt(0.1)(.9)/150 = -.82 Was your test one-tail upper tail, one-tail lower tail, or two-tail? Explain why you chose that kind of…
A major oil company has developed a new gasoline additive that is supposed to increase mileage. To test this hypothesis, ten cars are randomly selected. The cars are driven both with and without the additive. The results are displayed in the following table. Can it be concluded, from the data, that the gasoline additive does significantly increase mileage? Let d=(gas mileage with additive)−(gas mileage without additive)�=(gas mileage with additive)−(gas mileage without additive). Use a significance level of α=0.05�=0.05 for the test. Assume that the gas mileages are normally distributed for the population of all cars both with and without the additive. Car 1 2 3 4 5 6 7 8 9 10 Without additive 27.2 13.7 12.5 13.4 14.7 25.5 10.3 13.9 14.5 25 With additive 29.7 15.7 14.1 16.4 17.8 27.8 12.1 15 17.3 28 Copy Data Step 1 of 5: State the null and alternative hypotheses for the test.
A study of fox rabies in a country gave the following information about different regions and the occurrence of rabies in each region. A random sample of n1 = 16 locations in region I gave the following information about the number of cases of fox rabies near that location. x1: Region I Data 1 9 9 9 7 8 8 1 3 3 3 2 5 1 4 6 A second random sample of n2 = 15 locations in region II gave the following information about the number of cases of fox rabies near that location. x2: Region II Data 1 1 5 1 6 8 5 4 4 4 2 2 5 6 9 What is the value of the sample test statistic? (Test the difference μ1 − μ2. Do not use rounded values. Round your final answer to three decimal places.)
On each trial of an experiment, a subject is presented with a constant soft noise, which is interrupted at some unpredictable time by a noticeably louder sound. The time it takes for the subject to react to this louder sound is recorded. The following list contains the reaction times (in milliseconds) for the 15 trials of this experiment: 212, 236, 217, 235, 164, 257, 175, 285, 202, 193, 231,152, 269, 296, 186 Send data to calculator Find 30th and 75th percentiles for these reaction times.
A random selection of volunteers at a research institute have been exposed to a typical cold virus. After they started to have cold symptoms, 15 of them were given multivitamin tablets formulated to fight cold symptoms. The remaining 15 volunteers were given placebo tablets. For each individual, the length of time taken to recover from the cold is recorded. At the end of the experiment the following data are obtained. Days to recover from a cold Treated with multivitamin 4.9. 3.9, 4.9. 7.3, 3.7, 5.7, 4.3, 6.1, 4.9, 5.4, 7.7, 7.3, 4.6, 4.3, 4.6 Treated with placebo 5.1, 5.3, 5.3, 1.6, 1.6, 4.8, 4.4, 3.3, 3.7, 5.2, 5.5, 5.8, 6.5, 1.5, 5.4 Send data to calculator Send data to Excel It is known that the population standard deviation of recovery time from a cold is 1.8 days when treated with multivitamin tablets, and the population standard deviation of recovery time from a cold is 1.5 days when treated with placebo tablets. It is also known that both populations are approximately normally…
With two COVID-19 vaccines now in the final stages of approval for use in the U.S., 63% of Americans say they are willing to receive a COVID-19 vaccination approved by the Food and Drug Administration (FDA), up from 50% who said this in September. The December results came from a Gallup poll conducted Nov. 16-29, 2020, with a random sample of 2,968 adults. The September results came from a Gallup poll conducted Sept. 14-27, 2020, with a random sample of 2,730 adults. Does this data suggest that the share of Americans who say they plan to get vaccinated has increased? State and test the relevant hypotheses at significance level 0.10 by using the P-value method.
A manufacturing company employs two inspecting devices to sample a fraction of their output for quality control purposes. The first inspection monitor is able to accurately detect 99.5% of the defective items it receives, whereas the second is able to do so in 99.7% of the cases. Assume that four defective items are produced and sent out for inspection. Let X and Y denote the number of items that will be identified as defective by inspecting devices 1 and 2, respectively. Assume the devices are independent. Determine (a) the range of the joint probability distribution of X and Y. (b) fxy(*, y). (c) fx(x). (d) E(X). e) fy|x=3(y).