A viral test for COVID-19 determines when a patient is no longer infected. An antibody test determines if a person has had a previous infection. The U.S. National Institutes of Health recently did a study on nurses treating COVID-19 patients. None initially had COVID-19, and each nurse was then tested at the beginning of every day with an antibody test to determine if the nurse had become infected during the previous day. A total of 100 nurses tested positive during the study. As soon as one was infected, the nurse was given a daily viral test at the beginning of every day until no longer infected. The data for these 100 nurses is summarized below. Day n after infection 0 1 2 4 5 ... 19 20 21 # still infected 100 100 100 99 97 94 1 ... This data has become the basis for a Markov chain model of the infection time for COVID-19 patients. Let Xn, n = 0, 1, 2, .., 21 denote the number of days a patient has been continuously infected at the beginning of day n after infection until the patient is no longer infected. For this model, what are P3.4 and p19.0? For clarity, commas are used here between the states in the subscripts of the pi- 97/99, 1/3 O 97/99, 2/3 O 97/99, 1 O 2/99, 1/3

A viral test for COVID-19 determines when a patient is no longer infected. An antibody test determines if a person has had a previous infection. The U.S. National Institutes of Health recently did a study on nurses treating COVID-19 patients. None initially had COVID-19, and each nurse was then tested at the beginning of every day with an antibody test to determine if the nurse had become infected during the previous day. A total of 100 nurses tested positive during the study. As soon as one was infected, the nurse was given a daily viral test at the beginning of every day until no longer infected. The data for these 100 nurses is summarized below. Day n after infection 0 1 2 4 5 ... 19 20 21 # still infected 100 100 100 99 97 94 1 ... This data has become the basis for a Markov chain model of the infection time for COVID-19 patients. Let Xn, n = 0, 1, 2, .., 21 denote the number of days a patient has been continuously infected at the beginning of day n after infection until the patient is no longer infected. For this model, what are P3.4 and p19.0? For clarity, commas are used here between the states in the subscripts of the pi- 97/99, 1/3 O 97/99, 2/3 O 97/99, 1 O 2/99, 1/3

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 test of the quality of two television commercials , each commercial was shown in a separate test area six times over a one week period. The following week a telephone survey was conducted to identify individuals who had seen the commercials. Those individuals were asked to state the primary message in the commercials . The following results were recorded. Commercial A. Commerical b # who saw comm 155 204 # who recalled message 64. 63 Use a=0.05 and test the hypothesis that there is no difference in the recall proportions for the two commercials. What is the vaule of the test statistic ( to 2 decimal) What is the p value(to 4 decimal) Compute a 95% cofidence interval for the difference between the recall proportions for the two population (to 4 decimal) Thank you
Trematodes of the species Euhaplorchis californiensis may infect the California kill fish, Fundulus parvipinnis. Researchers have observed that infected fish spend excessive time near the water surface, where they may be more vulnerable to bird predation. Researchers set up an experiment in a large outdoor tank that stocked with three kinds of killifish, uninfected, lightly infected, and highly infected, and recorded the number of fish that is eaten by birds. State the null and alternative hypothesis
A study was performed to test the effectiveness of a new treatment for migraines. There were 125 patients in the study. Of these, 60 were randomly assigned to receive the standard treatment and 65 to receive the new treatment. All were instructed to take the medication at the onset of their next migraine and to notice if the pain of their migraine felt reduced after half an hour. Fifty patients receiving the new treatment reported reduced pain, compared with only 40 of the patients receiving the standard treatment. The results seem to favor the new treatment, but could the difference just be due to chance? In this problem, consider the null hypothesis that the percentage of patients with a reduction in pain is the same between the two treatments, versus the alternative hypothesis that the percentages are different. (a) Under the null hypothesis, the difference in the sample percentages is expected to be ___%. The standard error for the difference is estimated to be ___%. (b) Calculate…
A paper describes a study of the use of MRI (Magnetic Resonance Imaging) exams in the diagnosis of breast cancer. The purpose of the study was to determine if MRI exams do a better job than mammograms of determining if women who have recently been diagnosed with cancer in one breast have cancer in the other breast. The study participants were 950 women who had been diagnosed with cancer in one breast and for whom a mammogram did not detect cancer in the other breast. These women had an MRI exam of the other breast, and 101 of those exams indicated possible cancer. After undergoing biopsies, it was determined that 30 of the 101 did in fact have cancer in the other breast, whereas 71 did not. The women were all followed for one year, and four of the women for whom the MRI exam did not indicate cancer in the other breast were subsequently diagnosed with cancer that the MRI did not detect. The accompanying table summarizes this information. Cancer Cancer Not Present Present Total MRI…
High levels of cholesterol in the blood are associated with higher risks of heart attacks. Will using a drug to lower blood cholesterol reduce heart attacks? The Helsinki Heart Study recruited middle-aged men with high cholesterol but no history of other serious medical problems to investigate this question. The volunteer subjects were assigned at random to one of the two treatments: 2051 men took the drug gemfibrozil to reduce their cholesterol levels, and a control group of 2030 men took a placebo. During the next five years, 56 men in the gemfibrozil group and 84 in the placebo group had heart attacks. Is the difference statistically significant at the alpha = 0.01 level?
In the current pandemic, researchers are working on creating antibody tests to determine which individuals have already had an infection caused by the COVID-19 virus. If someone has been infected, then they will have certain antibodies in their system and the hope is that a highly accurate test can be created to detect these antibodies. Assume a researcher creates a new antibody test, which for individuals who are known to have had the infection in the past and thus truly have the COVID-19 antibodies, gives a positive result 95% of the time. This same test gives a negative result 90% of time for people who do not have the antibodies. Assume that COVID-19 has affected 5% of the population in the region of interest. What is the probability someone has NOT been infected previously given that their antibody test result comes back positive? [four decimals]
A study was conducted to determine whether big-city and small-town dwellers differed in their helpfulness to strangers. In this study, the investigators rang the doorbells of strangers living in a large City or small towns in the vicinity. They explained they had misplaced the address of a friend living in the neighbourhood and asked to use the phone. The following data show the number of individuals who admitted or did not admit the strangers (the investigators) into their homes: Helpfulness to strangers Admitted strangers into their home Didnot admit strangers into their home Big city dwellers 60 90 Small town dwellers 70 30 State the dependent and independent variable Is this a directional or non directional
A study compares students who use a website and students who do not use the website. In addition to asking the students in the samples about GPA, each student was also asked how many hours he or she spent studying each day. The two samples (141 students who were users of the website and 68 students who were not users of the website) were independently selected from students at a large, public university. Although the samples were not selected at random, they were selected to be representative of the two populations. n USE SALT For the sample of users of the website, the mean number of hours studied per day was 1.46 hours and the standard deviation was 0.83 hours. For the sample of students who do not use the website, the mean was 2.77 hours and the standard deviation was 0.99 hours. Do these sample data provide convincing evidence that the mean time spent studying for users of the website at this university is less than the mean time spent studying by students at the university who do…
To determine a target audience for a new email package, a computer company surveyed a sample of potential customers, asking each whether he/she uses email on a regular basis. considered "a regular basis" to be at least three times a week.) The data, as summarized table below, were classified according to two variables: the age of the respondent ("under 54", "55+") and regularity of email use ("on a regular basis" or "not on a regular basis"). Each cell of the table contains three numbers: the first number is the observed cell freque second number is the expected cell frequency (fF) under the assumption that there is no between age and regularity of email use and the third number is the following value. fo-fE) (Observed cell frequency - Expected cell frequency ) fE Expected cell frequency The numbers labeled "Total" are totals for observed frequency. Part 1
A cat-lover claims that cats are just as smart as dogs. In order to back this claim up with some evidence she organizes a study at a large local pet daycare center. A random sample of 40 cats are selected and a random sample of 40 dogs are selected. Each of the selected animals is given one hour with a trainer in which the trainer attempts to teach them to roll over. Upon conclusion of the training, the proportion of dogs and proportion of cats that have learned this skill is computed. The trainer reports that she is 90% confident that the true difference in the proportion of all dogs and all cats (pD – pC) that can learn this skill with one hour of training is between –0.05 to 0.28. Which of the following conclusions can be made based upon this confidence interval? (A) Because most of the values in the confidence interval are positive, this proves that dogs are smarter than cats. (B) Because the point estimate of the confidence interval is positive, there is convincing evidence…
We know that SARS-CoV-2 was circulating, perhaps widely, in southern California as early as the beginning of February 2020. Many cases, particularly in young people, are mild or even asymptomatic. Health clinics now provide antibody tests, which are tests for whether your immune system has previously been exposed to the SARS-CoV-2 virus and recovered. People who have these antibodies may have immunity to future exposure. Which of the following is/are synonymous with P(COVID-19)? a. Prevalence b. Specificity c. 1 - Specificity d. Sensitivity
A local school board believes there is a difference in the proportion of households with school-aged children that would support starting the school year a week earlier, and the proportion of households without school- aged children that would support starting the school year a week earlier. They survey a random sample of 40 households with school-aged children about whether they would support starting the school year a week earlier, and 38 households respond yes. They survey a random sample of 45 households that do not have school-aged children, and 25 respond yes. Let p3= the true proportion of households with school-aged children that would support starting the school year a week early and pw= the true proportion of households without school-aged children that would support starting the school year a week earlier. The P-value for this significance test is 0.000034. Which of the following is the correct conclusion for this test of the hypotheses Ho: P;- Pw=0 and H, P,- Pw0 at the a =…