There is an antigen kit for COVID-19.If a person is infected, the kit will correctiy report 989% of the time.If a person is not infected, the kit will incorrectly report that the person is infected 19% of thetime.The kit is used in two communities called A and B.A and B differ in the percentage of the infected individuals.In A, 98% of the people have no virus. In B, 70% of the people have no virus.Alice lives in A. Bob lives in B. Both Alice and Bob use the antigen kit. They both havepositive results. Compare their chances of actually having the virus.

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Answered: There is an antigen kit for COVID-19.…

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...

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You are interested in testing if there is a difference in weight-loss between 3 popular diet types; low calorie, low fat and low carb. Participants are randomly assigned one of the three groups or a control group. The control group will be told that are participating in a weight-loss study, but will not be following any particular diet. This is to study the placebo effect, weight-loss from just participating in the study. At the start of the study, each participant's weight is recorded in pounds. After 8 weeks they are weighed again, and the weight difference is recorded. A positive value represents a weight loss while a negative value represents a weight gain. Test at 5% significance. Round answers to 3 decimal places. Diet Type Low Calorie Low Calorie Low Calorie Low Calorie Low Calorie Low Fat Low Fat Low Fat Low Fat Low Fat Low Carb Low Carb Low Carb Low Carb Low Carb Control Control Control Control Control Pounds Lost 6.9 4.7 3.5 7.7 5.9 3.8 1.4 3.8 5.2 2 4.9 2.6 2.7 5.6 3.4 1.3…
Although a research study is typically conducted with a relatively small group of participants known as a most researchers hope to generalize their results to a much larger group known as a
Researchers are interested in determining if there is a difference in the proportion of women who choose the different types of treatments for those diagnosed with Ductal Carcinoma in Situ (DIS) breast cancer, which is a form of breast cancer that occurs in the Breast Ducts and has not spread. Following a diagnoses of DCIS, women can choose between three different treatment plans: a mastectomy or a lumpectomy followed by radiation therapy or a lumpectomy followed by Adjuvant Endocrine therapy. A random sample of 500 women diagnosed with DCIS breast cancer was obtained. Of the 500 women, 190 chose to have a mastectomy, 150 chose to have a lumpectomy followed by radiation, and 160 chose to have a lumpectomy followed by Adjuvant Endocrine therapy. At the 1% significance level, what conclusion can be reached?
The Stanford University Heart Transplant Study was conducted to determine whether an experimental heart transplant program increased lifespan. Each patient entering the program was officially designated a heart transplant candidate, meaning that he was gravely ill and might benefit from a new heart. Patients were randomly assigned into a treatment and control groups. Patients in the treatment group received a transplant and those in the control group did not. The table below displays how many patients survived and died in each group. control treatment alive 4 24 dead 30 45 Explain why we cannot construct a confidence interval or a hypothesis test (hint: consider the conditions).
A researcher found out that some coal miners in a community of 960 miners had anthracosis. He would like to find out what was the contributing factor for this disease. He randomly selected 500 men (controls) in that community and gave them a questionnaire to determine if they too had anthracosis. One hundred-fifty (150) of them reported that they mined coal, but did not have anthracosis. From those who had the disease, 140 were not coal miners. Calculate the measure of association between exposure to coal dust and development of anthracosis.
The traffic pattern is being analyzed for traffic going into Myrtle Beach on 501. The intersection of US-501 and US-17 Bypass was designed such that 50% of the traffic would continue straight on 501, 30% would go north on 17 Bypass, and 20% would go south on 17 Bypass. Since then, there has been a significant amount of commercial growth around the intersection that may have impacted the traffic flow. A sample of 600 cars is to be reviewed to see if the traffic has significantly changed using the chi-square test. How many cars do you expect to go straight on US-501?
You are interested in testing if there is a difference in weight-loss between 3 popular diet types; low calorie, low fat and low carb. Participants are randomly assigned one of the three groups or a control group. The control group will be told that are participating in a weight-loss study, but will not be following any particular diet. This is to study the placebo effect, weight-loss from just participating in the study. At the start of the study, each participant's weight is recorded in pounds. After 8 weeks they are weighed again, and the weight difference is recorded. A positive value represents a weight loss while a negative value represents a weight gain. Test at 10% significance. Round answers to 3 decimal places. Diet Type Low Calorie Low Calorie Low Calorie Low Calorie Low Calorie Low Fat Low Fat Low Fat Low Fat Low Fat Low Carb Low Carb Low Carb Low Carb Low Carb Control Control Control Control Control Pounds Lost 5.3 6.6 10.5 6.4 8.9 5 4 0.2 2.9 2.6 4.6 2.9 0.8 2.4 2.5 1.9…
A researcher wants to determine the specificity of mammograms to determine how effective they are at diagnosing women who have breast cancer. Assume the researcher obtained the results below from a study: Out of a total of 18 women with breast cancer, 12 screened positive and 6 screened negative on the mammogram. Out of a total of 82 women without breast cancer, 5 screened positive and 77 screened negative on the mammogram. Calculate and interpret the specificity of mammograms for detecting breast cancer.
A researcher randomly selected 158 personal vehicles and noted the type of vehicle and its color. The two-way table displays the data. A 5-column table with 4 rows. Column 1 has entries sedan, S U V, convertible, total. Column 2 is labeled Red with entries 14, 9, 20, 43. Column 3 is labeled Blue/Green with entries 31, 19, 6, 56. Column 4 is labeled Black/Gray with entries 22, 34, 3, 59. Column 5 is labeled Total with entries 67, 62, 29, 158. The columns are titled Vehicle color and the rows are titled vehicle type. Suppose a vehicle is randomly selected. Let event C = convertible and R = red. What is the value of P(R|C)? StartFraction 29 Over 158 EndFraction StartFraction 43 Over 158 EndFraction StartFraction 20 Over 43 EndFraction StartFraction 20 Over 29 EndFraction
A doctor wanted to study the effect of four different treatments on mental health. A group of 100 adults experiencing depression volunteered for the study. The doctor randomly assigned one-fourth of them to each of four groups. Group 1 followed a specific exercise plan, group 2 followed a specific diet plan, group 3 followed an exercise and diet plan, and group 4 did not follow any plan. After 4 weeks, the doctor contacted each participant and asked them if they felt any better. The results are displayed in the table. The doctor would like to know if these data provide convincing evidence that the distribution of responses differs across the treatment groups in the population of all patients like these. The random condition is met. The 10% condition is not needed because random sampling did not take place. This table of expected counts shows that all expected counts are at least 5. What is the value of the chi-square test statistic? χ‑2 = 5.03 χ‑2 = 6.26 χ‑2 = 25.33 χ‑2 = 39.22

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