Mammography and clinical breast examination are the two major techniques used to screenfor breast cancer. However, as true for any screening test, they are not completely accurate.If it is determined, based on mammographic findings, that there is a possibility of breastcancer, this is usually confirmed or disconfirmed by a subsequent biopsy. A false positive testis a mammogram positive test that is disconfirmed by biopsy. The data in Table 1 werereported in a paper concerning breast cancer screening (Elmore, et al, New England Journalof Medicine 1998; 338(16): 1089-1096).Table 1 False positive breast cancer screening tests over a 10-year period# Screening tests# False positive tests97626311. Another aspect of mammographic screening is the presence of false negatives. A false negativeis a screen negative woman who has breast cancer.False negatives usually occur because the tumors are small and hard to detect. It is estimatedthat among women with breast cancer, 2% of all screening tests are false negatives.Suppose that there are 100 women who have breast cancer. What is the probability that at least3 of them will not be detected by a mammogram?

Given that among women with breast cancer, 2% of all screening tests are false negatives.

Answered: Mammography and clinical breast…

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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One study of cell phones and the risk of brain cancer looked at a group of 469 people who have brain cancer. The investigators then asked about the use of cell phones. Result: “Our data suggest that the use of hand- held cellular phones is not associated with risk of brain cancer. B . Based on this study, can you determine that cellular use does not CAUSE brain cancer? Why or why not?
Using the latest in medical technology, an orthopedic doctor has developed a new surgical procedure that he believes is an improvement over the standard procedure. He wants to study whether the mean recovery time of patients who have the new procedure is less than the mean recovery time of patients who have the standard procedure. The doctor studies a random sample of 11 patients who have the new procedure and a random sample of 10 patients who have the standard procedure. (These samples are chosen independently.) The doctor records each patient's recovery time (in days). These data are shown in the table. Recovery times (in days) 350, 284, 291, 393, 295, 377, 401, 371, 423, 449, 364 New procedure Standard procedure 435, 409, 419, 423, 388, 410, 412, 438, 396, 424 Send data to calculator Send data to Excel Assume that the two populations of recovery times are approximately normally distributed. Can the doctor conclude, at the 0.01 level of significance, that the population mean of the…
In the early 1970s, a young man challenged an Oklahoma state law that prohibited the sale of 3.2% beer to males under age 21 but allowed its sale to females in the same age group. The case (Craig v. Boren, 429 U.S. 190, 1976) was ultimately heard by the U.S. Supreme Court. The state of Oklahoma argued that the law improved traffic safety. One of the three main pieces of data presented to the court was the result of a “random roadside survey.” This survey gathered information on gender and whether or not the driver had been drinking alcohol in the previous 2 hours. A total of 619 drivers under 21 years of age were included in the survey. The chi-square test statistic is approximately 1.64 for this data. Find the P-value State a conclusion at a 5% level of significance. Do you think that the data supports the Oklahoma law that forbids sale of 3.2% beer to males and permits it to females? See image.
The impact of a low-calorie diet on laboratory mice's longevity is being investigated by a medical researcher. Twenty mice are split into two groups (E and F) by random. A typical diet is given to Group E, while Group F is given a diet that only contains 70% as many calories as Group E's diet. The length of life (in days) of each mouse over the 36-month trial is documented. Table 2 provides the data that was obtained. The symbol of double star (**) signifies that the mouse was still alive at the end of the investigation. (a) (b) (c) Table 2: The length of life (in days) of each mouse Group E 900 907 751 833 920 787 830 877 848 901 Group F 1037 905 1023 988 1078 1011 ** 1063 898 1033 State a suitable null and alternative hypotheses for the problem. At 5% significance level, test the hypotheses in part (a) by using an appropriate nonparametric test. Write your conclusion.
A researcher is studying the effects of his newly created lens on vision. He samples 9 people with poor vision and measures their visual distance (in feet) with the lens and then without the lens. Did people’s vision with the lens differ from their vision without? Participant # With Lens Without Lens 1 8 14 2 6 17 3 9 12 4 7 11 5 5 12 6 9 18 7 8 13 8 9 7 9 7 13 What kind of analysis will you use? Why? State the null and alternative hypothesis. Check your assumptions. Explain why each of them are or are not met. Sketch a distribution and shade the rejection region(s), including the corresponding critical value(s). Using R, calculate your test statistic and interpret the results of your test. (Don’t forget your 95% confidence interval and screenshots of your work!) What do you conclude about the null hypothesis? Are there significant differences?
st is 22. Oishi and Shigehiro (2010) report that people who move from home to home frequently as children tend to have lower than average levels of well-being as adults. To further examine this relationship, a psychologist obtains a sample of n = 12 young adults who each experienced 5 or more different homes before they were 16 years old. These participants were given a standardized well-being questionnaire for which the general population has a
You may need to use the appropriate appendix table or technology to answer this question. Approximately 50% of all caregivers of older adults are caring for someone with memory loss (due to is percentage of caregivers caring for older adults with memory loss. This year, in a random sample of 400 caregivers, 181 were caring for older adults with memory loss uch as Alaheimer's or dementia). It is beleved that there has been a reduction in the (a) State the null and the alternative hypotheses. (Enter t for as needed.) (b) At the 0.05 level using the critical value approach, determine if there has been a significant reduction in the proportion of caregivers caring for adults with memory loss Compute the test statistk. Determine the critical value(s) for this test. (Round your answerta) to two decimal places. If the test is one-taled, enter NONE for the unused tal.) test statisticS test statistic State your condusion. O Reject Ha There is insufficient evidence to support the claim that the…
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Anterior cruciate ligament (ACL) injuries occur most frequently in planting and cutting sports such as basketball, soccer, and volleyball. National collegiate athletic association injury data show that female athletes injure the ACL more frequently than their male counterparts do. A sports medicine professor wants to test this claim. He surveyed 5 universities that had both men's and woman's basketball, soccer, and volleyball and asked them how many grade 3 ACL tears they had during the past 5 seasons. Using the following results, are women at greater risk than men for ACL injuries? (use a standard deviation of 0.01, one tail test). Women- 4,3, 5, 2,4 Men- 2, 0, 1 ,2, 1 What is the difference between a repeated measure study and a matched pairs study?
According to the American Lung association, lung cancer account for 28% of all cancer deaths in the US. A new type of screening for lung cancer, computed tomography (CT), has been developed. Medical researchers believe CT scans are scans are more sensitive than regular X-rays in pinpointing small tumors. The Cancer Center at the University of South Florida is currently conducting a clinical trial of 50,000 smokers nationwide to compare the effectiveness of CT scans with X-ray for detecting lung cancer (Today’s Tomorrows, Fall 2002). Each participating smoker is randomly assigned to one of the two screening methods, CT or chest X-ray, and his or her progress is tracked over time. The age at which the scanning method first detects a tumor is the variable of interest. A. Identify the data collection method used by the cancer researchers. B. dentify experimental units of the study. C. Identify the type of the variable measured. D. Identify the population and sample.
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Mammography and clinical breast examination are the two major techniques used to screen for breast cancer. However, as true for any screening test, they are not completely accurate. If it is determined, based on mammographic findings, that there is a possibility of breast cancer, this is usually confirmed or disconfirmed by a subsequent biopsy. A false positive test is a mammogram positive test that is disconfirmed by biopsy. The data in Table 1 were reported in a paper concerning breast cancer screening (Elmore, et al, New England Journal of Medicine 1998; 338(16): 1089-1096). Table 1 False positive breast cancer screening tests over a 10-year period # Screening tests # False positive tests 9762 631 1. Suppose 10 women are given mammograms. What is the probability that at least 1 woman will have a false positive test?

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