The table below shows the results of using X-ray imaging as a diagnostic test for tuberculosis in patientswith known TB status. Use it to answer the questions below.Test for TBTB absentTB presentNegative1739Positive5122Use this table to calculate the sensitivity and specificity of the test. Suppose that you have theknowledge that the prevalence of TB in a population is P(D) = 0.001, use the previously calculatedsensitivity and specificity to answer the following questions about testing a patient from the population(not those used in the study in the table.)1. Using the law of total probability, calculate P(Pos), the probability that a randomly chosen personfrom the population tests positive for the disease and P(Neg), the probability that a randomly chosenperson tests negative for the disease.2. Using Bayes' formula, find the probability that a patient who tested positive has the disease P(D |Pos) and the probability that a patient who tested negative is healthy P(H | Neg).3. If the disease prevalence were P(D) =0.5, repeat the calculations to find the new P(D | Pos) and P(H |Neg).

Answered: Image /qna-images/answer/d72c3e1f-9ced-4eca-a423-136741fccc41.jpg

Answered: The table below shows the results of…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 25EQ

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A new cream that advertises that it can reduce wrinkles and improve skin was subject to a recent study. A sample of 4949 women over the age of 50 used the new cream for 6 months. Of those 4949 women, 3333 of them reported skin improvement(as judged by a dermatologist). Is this evidence that the cream will improve the skin of more than 6060% of women over the age of 50? Test using ?=0.05α=0.05. test statistics ?=z= rejection region ?>z>
A test of body reaction to the Malaysian citizens who have taken their vaccine was conducted.Selected citizens who got side effect are categorised according to their blood type and the typeof vaccine received. From a sample of 250 citizens, 150 of them were administered withSinovac while the rest received AstraZeneca. Table 4 shows the number of citizens who hadside effect after being vaccinated. i) Complete Table 4 by finding the values of M and N. ii) Does different blood type among people who had side effect relate to the type of vaccinereceived at a=0.025?
In a study of tooth paste, 40 children used paste without fluoride resulting in a mean of 5.65 cavities with s1=1.3 . 40 children used paste with fluoride and this sample revealed mean of 4.75 cavities with s2=1.1. Do these results indicate a significant difference between two groups? Perform two-sided test at 2% SL, give all steps of procedure, interpret obtained result in terms of given example.
Data from a recent year showed that 55% of the tens of thousands of applicants to a certain program were accepted. A company that trains applicants claimed that 135 of the 240 students, it trained that year were accepted. Assume these trainees were representative of the population of applicants. Has the company demonstrated a real improvement over the average? What is the P-value?
What is the MS between and MS within? what is the MS subject? what is the Sm (needed in the Tukey test)
A researcher would like to examine how the chemical tryptophan, contained in foods such as turkey, can affect mental alertness. A sample of n = 9 college students is obtained, and each student’s performance on a familiar video game is measured before and after eating a traditional Thanksgiving dinner including roast turkey. The average score dropped by MD = 14 points after the meal with SS = 1152 for the difference scores. What type of t-test would you have to conduct in this scenario?Are the data sufficient to conclude that the treatment has a significant effect? Use a two-tailed test with α = .05. State the hypothesis, find the critical region, calculate your test statistic, and evaluate your hypothesis then calculate the Cohen’s d measure for this scenario. State whether this is a weak, moderate, or strong effect.
Calculate the X² statistic then compare it with the critical value to determine if we will reject or fail to reject the null hypothesis that "There is no difference in the proportion of students that choose STEM, Social Sciences and Liberal Arts"
A researcher is testing the effect of a new cold and flu medication on reaction time. A sample of n = 16 students is obtained and each student is given the normal dose of the medicine. Thirty minutes later, each student's reaction time is measured. The scores for the sample averaged M = 220 milliseconds with SS = 6000. Assuming that reaction time for students in the regular population averages μ = 200 milliseconds, are the data sufficient to conclude that the medication has a significant effect on reaction time? Test at the .05 level of significance. Make a point estimate and a 95% confidence interval estimate for the treated population mean.
A new cream that advertises that it can reduce wrinkles and improve skin was subject to a recent study. A sample of 60 women over the age of 50 used the new cream for 6 months. Of those 60 women, 50 of them reported skin improvement(as judged by a dermatologist). Is this evidence that the cream will improve the skin of more than 40% of women over the age of 50? Test using α=0.05 test statistics z=? rejection region z>? The final conclustion is A. We can reject the null hypothesis that p=0.4 and accept that p>0.4 That is, the cream can improve the skin of more than 40% of women over 50.B. There is not sufficient evidence to reject the null hypothesis that p=0.4 That is, there is not sufficient evidence to reject that the cream can improve the skin of more than 40% of women over 50.
The average drying time of a manufacturer’s paint is 20 minutes. Investigating the effectiveness of a modifica-tion in the chemical composition of her paint, the manu-facturer wants to test the null hypothesis μ = 20 minutes against a suitable alternative, where μ is the average dry-ing time of the modified paint. (a) What alternative hypothesis should the manufactureruse if she does not want to make the modification in thechemical composition of the paint unless it decreases thedrying time?(b) What alternative hypothesis should the manufactureruse if the new process is actually cheaper and she wants tomake the modification unless it increases the drying timeof the paint?
The personality trait of "Conscientiousness" (someone who is organized, responsible, and can control their impulses) has μ = 120 and σ =9. Test whether ARC students (n = 9, M = 126) differ on Conscientiousness. α = .05. Does the z score for the sample mean lie in the critical region (beyond the critical boundary)?
A test of body reaction to the Malaysian citizens who have taken their vaccine was conducted. Selected citizens who got side effect are categorised according to their blood type and the type of vaccine received. From a sample of 250 citizens, 150 of them were administered withSinovac while the rest received AstraZeneca. Table 4 shows the number of citizens who had side effect after being vaccinated. (Question & Table at images)

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