A new, simple test has been developed to detect a particular type of cancer. The test must be evaluated before it is put into use. A medical researcherselects a random sample of 1,000 adults and finds (by other means) that 3% have this type of cancer. Each of the 1,000 adults is given the test, andit is found that the test indicates cancer in 99% of those who have it and in 2% of those who do not. Based on these results, what is the probability ofa randomly chosen person having cancer given that the test indicates cancer? Of a person having cancer given that the test does not indicatecancer?.....Based on these results, what is the probability of a randomly chosenperson having cancer given that the test indicates cancer?(Round to three decimal places as needed.)What is the probability of a person having cancer given that the test doesnot indicate cancer?(Round to six decimal places as needed.).....

It is given that 3% have the type of cancer. that is, PCancer=0.03, it is also found that the test…

Answered: A new, simple test has been developed…

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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Travelers who have no intention of showing up often fail to cancel their hotel reservations in a timely manner. These travelers are known, in the parlance of the hospitality trade, as “no-shows”. To protect against no-shows and late cancellations, hotels invariably overbook rooms. A recent study examined the problems of over-booking rooms in the hotel industry. The following data, extracted from the study represent the daily numbers of late cancellations and no-shows for a random sample of 10 days at a hotel: 18, 16, 16, 16, 14, 18, 16, 18, 14, 19. a) Compute s, the sample s.d. for the data set
In a study to compare two different methods of teaching reading, a class of 20 children was divided into two groups at random. Each group was taught reading using one method. After six months the two groups were given the same test. One pupil in the first group was ill and missed the test. The scores are given below.Method 1 80 85 79 81 89 73 50 71 76Method 2 79 62 75 68 62 73 76 81 73 61(a) Calculate the extreme values and the quartiles for each group. (b) Hence draw box-and-whisker plots for the two groups using the same scale. (c) Comment on the differences between the two groups.
A researcher is interested in the amount of sleep an individual receives after consuming a sleeping aid (Melatonin, Valerian root, and Placebo). The researcher randomly selects individuals into either group. However, some individuals drop out of the study which results in unequal sample sizes. Melatonin Valerian Placebo n=6 n=10 n=4 N=20 M=14 M=13 M=9 G=250 T=84 T=130 T=36 ΣX2=3377 SS=60 SS=90 SS=37 a. Using symbols, state the hypotheses for a two-tailed test with α=0.05. b. Locate the critical region. In doing so, determine the degrees of freedom values. c. Calculate the F-ratio.
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As products come off a large assembly line, they are inspected for quality. They are placed into one of three categories: pass, fail, or need additional inspection. The manager claims that 80% of the products pass the inspection, 5% fail, and 15% need additional inspection. In an effort to increase the passing rate, the machines are recalibrated. After this recalibration, a random sample of 100 products is selected. It is discovered that 85 passed inspection, 2 failed, and 13 needed additional inspection. The manager would like to know if there is convincing evidence that the distribution has changed. What is the value of the chi-square test statistic and P-value? Find the chi-square table here. χ2 = 2.38, P-value is less than 0.0005 χ2 = 2.38, P-value is greater than 0.25 χ2 = 5.10, P-value is less than 0.0005 χ2 = 5.10, P-value is greater than 0.25
Public Agenda conducted a survey of 1379 parents and 1342 students in grades 6-12 regarding the importance of science and mathematics for success in life after school. 50% of the students thought these skills were essential and 62% of the parents thought these subjects were crucial for success. The two random samples were selected independently of each other. Is there enough evidence to conclude that the proportion of parents who feel science and math are important for success is higher than the proportion of students who feel the same way? Conduct your test with a level of significance of 0.05.
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Dr. Sloane is doing a study to test the association between alcohol consumption and the occurrence of cancer of the liver. He chooses a hospital-based sample and collects all newly diagnosed cases of histologically confirmed liver cancer diagnosed at that hospital. For his control group, he reviews the charts of all patients coming through all the clinics at this hospital who are not diagnosed with liver cancer. He makes sure that the cases and controls are similar by age and sex. A. Looking at the odds ratios and the p-values together, describe your observations. B. Looking at the p-values, what do they tell you about the strength of the association between drinking different amounts of alcohol per day and the risk of having liver cancer?
A local school board wants to estimate the 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 30 households respond yes. They survey a random sample of 45 households that do not have school-aged children, and 25 respond yes. Assuming the conditions for inference have been met, what is the 90% confidence interval for the difference in proportions of households that would support starting the school year a week earlier? Find the z-table here. 0.75(1-0.75), 0.56(1-0.56) O (0.75 - 0.56) ±1.65 45 40 0.75(1-0.75) 0.56(1-0.56) O (0.75 - 0.56) ±1.96, 85 85 O (0.75 - 0.56) ±1.65, 0.75(1-0.75) 0.56(1-0.56) + 40 45 O (0.75 - 0.56) ±1.96 0.75(1-0.75)…

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