A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Related questions
Question
One of the tests for Covid-19 is a genetic test, the aim of which is to detect viral RNA. If this test is applied during Stage 1, it will not detect the virus since the virus is hidden away inside the patient’s cells. 2% of patients with respiratory symptoms whose test indicates the presence of the SARS-Cov2, do not in fact have the SARS-Cov2, due to errors in the way the test is conducted. If this test is applied during Stage 2, it should detect SARS-Cov2 but 3% of these tests fail to detect SARS-Cov2 also due to errors in the way the test is conducted.
a) Write the 2% and 3% probabilities using conditional
b) Are the 2% and 3% an example of a false positive rate or a false negative rate or neither?
c) Is it possible to estimate the false negative probability of the genetic test by applying the test to patients known to be in Stage 3 of Covid-19?
d) Is it possible to estimate the false positive probability by applying the test to patients known to be in Stage 3 of Covid-19?
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by stepSolved in 3 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.Similar questions
- Twenty middle-aged men with glucose readings between 90 milligrams per deciliter and 120 milligrams per deciliter of blood were selected randomly from the population of similar male patients at a large local hospital. Ten of the 20 men were assigned randomly to group A and received a placebo. The other 10 men were assigned to group B and received a new glucose drug. After two months, posttreatment glucose readings were taken for all 20 men and were compared with pretreatment readings. The reduction in glucose level (Pretreatment reading − Posttreatment reading) for each man in the study is shown here. Group A (placebo) reduction (in milligrams per deciliter): 12, 8, 17, 7, 20, 2, 5, 9, 12, 6 Group B (glucose drug) reduction (in milligrams per deciliter): 29, 31, 13, 19, 21, 5, 24, 12, 8, 21 Part A: Do the data provide convincing evidence, at the α = 0.02 level, that the glucose drug is effective in producing a reduction in mean glucose level? Part B: Create and interpret a 98%…arrow_forwardA group of 30 postmenopausal women were given oral conjugated estrogen for one month.Plasma levels of plasminogen-activator inhibitor type 1 (PAI-1) went down for 22 of the women, but went up for 8 women.15 Use a sign test to test the null hypothesis that oral conjugated estrogen has no effect on PAI-1 level.Use α=0.10 and use a nondirectional alternative.arrow_forwardA study was conducted that investigated the gene ACTN3, which encodes a protein that functions in fast-twitch muscle fibres. People can be classified according to which genotype of this gene they have, RR, RX or XX. The study included a sample of elite sprinters and a sample of endurance athletes. The researchers are investigating whether there is an association between the genotype classification and the type of athlete (sprinters or endurance). What type of hypothesis test would be appropriate for this study? Explain your answer in one or two sentences.arrow_forward
- Based on advancements in drug therapy, a pharmaceutical company is developing Resithan, a new treatment for depression. A medical researcher for the company is studying the effectiveness of Resithan as compared to their existing drug, Exemor. A random sample of 461 depressed individuals is selected and treated with Resithan, and 172 find relief from their depression. A random sample of 419 depressed individuals is independently selected from the first sample and treated with Exemor, and 121 find relief from their depression. Based on the medical researcher's study can we conclude, at the 0.01 level of significance, that the proportion p1 of all depressed individuals taking Resithan who find relief from depression is greater than the proportion p2 of all depressed individuals taking Exemor who find relief from depression? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as…arrow_forwardI read about an antiviral drug called Paxlovid which can be given to high-risk individuals early after exposure to Covid-19 and is said to be protective against serious illness. A group of 1219 high-risk people were selected and 607 were given Paxlovid and 612 were given a placebo. After 28 days, nobody given Paxlovid had died and 6 were hospitalized. Among the placebo group, 10 had died and 41 were hospitalized. Our goal is to compare the difference in these proportions and assess the significance of the differences. We will add the steps as we go. What makes sense as a null hypothesis and alternative hypothesis? 2. What would be a good level of significance, and what is the critical value?arrow_forwardA study was conducted that investigated the gene ACTN3, which encodes a protein that functions in fast-twitch muscle fibres. People can be classified according to which genotype of this gene they have, RR, RX or XX. The study included a sample of elite sprinters and a sample of endurance athletes. The researchers are investigating whether there is an association between the genotype classification and the type of athlete (sprinters or endurance). Observed counts XX RX RR Total Endurance 55 49 30 134 Sprinters 49 95 50 194 Total 104 144 80 328 The observed test statistic was 9.38 (2dp) and the associated p-value was 0.009192 (6dp). Make a decision and conclusion for this hypothesis test in context. Use a significance level of 1% (α = 0.01).arrow_forward
- 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 ?arrow_forwardA study was conducted that investigated the gene ACTN3, which encodes a protein that functions in fast-twitch muscle fibres. People can be classified according to which genotype of this gene they have, RR, RX or XX. The study included a sample of elite sprinters and a sample of endurance athletes. The researchers are investigating whether there is an association between the genotype classification and the type of athlete (sprinters or endurance). What is the null and alternative hypotheses for the test?arrow_forwardA study was conducted that investigated the gene ACTN3, which encodes a protein that functions in fast-twitch muscle fibres. People can be classified according to which genotype of this gene they have, RR, RX or XX. The study included a sample of elite sprinters and a sample of endurance athletes. The researchers are investigating whether there is an association between the genotype classification and the type of athlete (sprinters or endurance). Observed counts XX RX RR Total Endurance 55 49 30 134 Sprinters 49 95 50 194 Total 104 144 80 328 What degrees of freedom should be used for this test? Explain in one or two sentences how you calculated your answer.arrow_forward
- 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.arrow_forwardluyckx et al. 2012 discovered that resistances to the bacterial parasite Pasteuria ramosa is genetically variable in the common freshwater crustacean Daphnia magna. to investigate the genetic basis of this cariation, they crossed a completely resistant lineage to a completely susceptible lineage. All the F1 offspring were resistant. these offspring, when mature, were then crossed to each other to produce an F2 generation. if resistance is the result of only a single gene with 2 forms (alleles), then resistant and suspectible F2 offspring should occur in a 3:1 ratio. of 71 F2's tested,57 were resistant and 14 were susceptible. Answer these Q's: a) calculate the range of most-plausible values for the proportion of resistant offspring. Does the plausible range include the proportion predicted if resistence is determined by a single gene? b.) give two other values for the proportion that are also consistent with the data. c.) test the genetic hypothesis. Are the results compatible with…arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:9780134753119
Author:Sheldon Ross
Publisher:PEARSON