QUESTION 13The test for screening donated blood for the presence of the AlDS virus was developed in the 1980s. It is designed to detect antibodies, substancesproduced by the body of donors carrying the virus, however it is not 100% accurate. The developer of the test claimed that the test would produce fewerthan 5% false positives and fewer than 1% false negatives. In order to evaluate the accuracy of the test 1000 persons known to have AlDS and 10,000persons known to not have aids were given the test. The following results were tabulated:True State of PatientTest ResultHas AidsDoes Not Have AidsTotalPositive Test9975301,527Negative Test3.9,4709,473Total1.00010,000000 1,00010,00011,000Totalconclusion.Is there significant evidence that the test produces less than 1% false negatives. Report the p-value and yourO p-value=D0.052>0.05%3DaFail to reject Ho: There is insufficient evidence that the test produces less than 1% false negativesO p-value=1.000>0.053Da→ Fail to reject Ho: There is insufficient evidence that the test produces less than 1% false negativesO p-value=D0.026<0.05%3Da Reject Ho: There is significant evidence that the test produces less than 1% false negativesO p-value=D0.013<0.05%3a Reject Ho: There is significant evidence that the test produces less than 1% false negatives

Introduction: Suppose p is the true proportion of false negatives results produced by the test.

Answered: QUESTION 13 The test for screening…

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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Please give an answer with a calculation and give an explanation of the correct and incorrect option.
A pharmaceutical company proposed a vaccine that would combat paralytic polio. Two independent random samples were collected from the population. One random sample of 201,229 was given the placebo, and among them 100,910 contracted paralytic polio. The other random sample of 200,745 was given the vaccine, and among them 50,033 people ended up contracting paralytic polio. Let the true proportion of cases of paralytic polio given placebo be p1p1 and the true proportion of cases of paralytic polio given vaccine be p2. Calculate the upper bound of a 95% confidence interval for p1−p2. Round your answer to three decimal places.
disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Now suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 223 numerical entries from the file and r = 48 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1.(i) Test the claim that p is less than 0.301. Use ? = 0.05. (a) What is the level of significance?State the null and alternate hypotheses. H0: p < 0.301; H1: p = 0.301H0: p = 0.301; H1: p > 0.301 H0: p = 0.301; H1: p < 0.301H0: p = 0.301; H1: p ≠ 0.301 (b) What sampling distribution will you use? The standard normal, since np > 5 and nq > 5. The standard normal, since np < 5 and nq <…
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…
A researcher is creating a new treatment protocol for Myelodysplastic Syndrome (MDS), a form of preleukemia. Following the old treatment protocol, 28% of patients with MDS will develop leukemia within 5 years of MDS diagnosis. He believes his new treatment protocol will lead to fewer MDS patients developing leukemia. He takes a random sample of 100 individuals on his new treatment protocol. Of these 100 individuals, 20 develop leukemia within 5 years of MDS diagnosis. In questions 8-9, create a 98% confidence interval for the true proportion of all MDS patients on this new treatment who will develop leukemia within 5 years of MDS diagnosis. What is the confidence interval? Do not round your answer. What is the interpretation of your confidence interval?
question 4 Diagnostic tests of medical conditions can have several types of results. The test resultcan be positive or negative, whether or not a patient has the condition. A positive test (+)indicates that the patient has the condition. A negative test (-) indicates that the patientdoes not have the condition. Remember, a positive test does not prove that the patient hasthe condition. Additional medical work may be required. Consider a random sample of200 patients, some of whom have a medical condition, and some of whom do not. Resultsof a new diagnostic test for the condition are shown. Condition ispresent Condition is absent total Test result (+) 110 20 130 Test result (-) 20 50 70 total 130 70 200 Assume the sample is representative of the entire population. For a person selected at random,compute the following probabilities:a. P(+│condition is present); this is known as the sensitivity of a test. b. P(- │condition is absent); this is known as the…
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?
2) A local home inspector wants to test for lead levels in 10 homes using two different testing methods in each of the homes to determine the level of lead in each of the homes. Two different tests (A and B) are used to determine the level of lead found in each of ten randomly selected homes. The home inspector believes that Test A is more accurate than Test B. The data obtained, for lead level in each home using each method is shown in the table below. SPECIMEN 8| 9 2 3 4 6 7 10 A 22.7 23.6 24.0 26.6 27.2 28.7 35.0 32.5 44.1 47.3 Test B 23.0 23.2 23.5 25.6 27 27.1 33.2 35.3 40.5 47.8 a. Does this data provide convincing evidence to support the home inspectors claim? Provide a statistical justification to support your answer. b. What kind of error could you have made? What is one consequence of that error? c. Is the sample statistically significant at the 0.05 level? If not, at what significance level would these results be statistically significant at?
In the largest clinical trial ever conducted, 401,974 children were randomly assigned to two groups. The treatment group consisted of 201,229 children given the Salk vaccine for polio, and the other 200,745 children were given a placebo. Among those in the treatment group, 33 developed polio, and among those in the placebo group, 115 developed polio. If we want to use the methods for testing a claim about two population proportions to test the claim that the rate of polio is less for children given the Salk vaccine, are the requirements for a hypothesis test satisfied? Explain. Choose the correct answer below. ……… O A. The requirements are satisifed; the samples are simple random samples that are independent, and for each of the two groups, the sample size is at least 1000. O B. The requirements are satisfied; the samples are simple random samples that are independent, and for each of the two groups, the number of successes is at least 5 and the number of failures is at least 5. O C.…
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In the largest clinical trial ever conducted, 401,974 children were randomly assigned to two groups. The treatment group consisted of 201,229 children given the Salk vaccine for polio, and the other 200,745 children were given a placebo. Among those in the treatment group, 33 developed polio, and among those in the placebo group, 115 developed polio. If we want to use the methods for testing a claim about two population proportions to test the claim that the rate of polio is less for children given the Salk vaccine, are the requirements for a hypothesis test satisfied? Explain. A The requirements are not satisfied; the samples are not simple random samples that are independent. B. The requirements are satisfied; the samples are simple random samples that are independent, and for each of the two groups, the number of successes is at least 5 and the number of failures is at least 5. C. The requirements are satisifed; the samples are simple random samples…
A large company that produces a "tat-burner pill claims an average Ioss of 20 pounds in the first month. A consumer advocacy group believes that this claim is actually just "hype" intended to sell more of the compound. The advocacy group Would like to obtain statistical evidence about this issue and takes a random sample of 100 consumers who responded that they had purchased the pill but didn't know what the survey was about. They find that these 100 people lost an average of 18 pounds. Let the standard deviation of the population be 7.5 pounds. Clearly state the hypotheses, obtain the test statistic and p-value, and state the decision and conclusion. Show all your work.

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