1. For a certain disease, a new test is proposed based on the occurrence of a specific protein X in the blood of patients. Inother words, this test gives a positive result if the protein X is found in the blood of the tested individual. Accordingto this new test performed in a subpopulation composed of healthy people and people with this disease, it was reportedthat among the patients with this disease, there were 95% who had the protein X. On the other hand, the protein X waspresent only in 30% among the healthy subgroup. The general incidence of this disease among the population is known tobe 10 percent, which is determined from various surveys over the years. From this data, derive a probabilistic measure todetermine the accuracy of this test. Please briefly comment on your results.

Given : Let D be the event representing the patients with the disease and H be the event…

Answered: 1. For a certain disease, a new test is…

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

The National Academy of Science reported that 41% of research in mathematics is published by US authors. The mathematics chairperson of a prestigious university wishes to test the claim that this percentage is no longer 41%. He has no indication of whether the percentage has increased or decreased since that time. He surveys a simple random sample of 186 recent articles published by reputable mathematics research journals and finds that 92 of these articles have US authors. Does this evidence support the mathematics chairperson’s claim that the percentage is no longer 41%? Use a 0.05 level of significance. Step 1 of 3: State the null and alternative hypotheses for the test. circle the answer below. H0 p=0.41 ha: p⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯0.41 A.<B.≠C.> Step 2 of 3: Compute the value of the test statistic. Round your answer to two decimal places Step 3 of 3: Draw a conclusion and interpret the decision. A. We reject the null hypothesis and conclude that there is insufficient evidence at a…
A study used 1259 patients who had suffered a stroke. The study randomly assigned each subject to an aspirin treatment or a placebo treatment. During a 3-year follow-up period, in Sample 1, 634 people received placebo treatments and 25 people died from heart attack. In sample 2, 625 people received aspirin treatment and 18 died from heart attack. Let pl denote the population proportion of death from heart attack for those with no treatment and p2 denote the population proportion of death from heart attack for those with aspirin treatment. (c) Which of SEO and SE1 is used for calculating a confidence interval for comparing two population proportions? Which is used for calculating the test statistic in a hypothesis test? (d) Construct the 95% confidence interval for pi – p2. Interpret.
A random sample of n1 = 157 people ages 16 to 19 were taken from the island of Oahu, Hawaii, and 12 were found to be high school dropouts. Another random sample of n2 = 129 people ages 16 to 19 were taken from Sweetwater County, Wyoming, and 6 were found to be high school dropouts. Do these data indicate that the population proportion of high school dropouts on Oahu is different (either way) from that of Sweetwater County? Use a 1% level of significance. (a) What is the level of significance? What is the value of the sample test statistic? (Test the difference p1 − p2. Do not use rounded values. Round your final answer to two decimal places.) (c) Find (or estimate) the P-value. (Round your answer to four decimal places.)
The National Academy of Science reported that 33 % of research in mathematics is published by US authors. The mathematics chairperson of a prestigious university wishes to test the claim that this percentage is no longer 33 %. He has no indication of whether the percentage has increased or decreased since that time. He surveys a simple random sample of 280 recent articles published by reputable mathematics research journals and finds that 108 of these articles have US authors. Does this evidence support the mathematics chairperson's claim that the percentage is no longer 33 % ? Use a 0.01 level of significance. Step 1 of 3: State the null and alternative hypotheses for the test. Fill in the blank below. Answer Ho :p = 0.33 Ha P O # ο ο ο HAV O < 0.33 Tables Keypad Keyboard Shortcuts
A random sample of n1 = 148 people ages 16 to 19 were taken from the island of Oahu, Hawaii, and 14 were found to be high school dropouts. Another random sample of n2 = 125 people ages 16 to 19 were taken from Sweetwater County, Wyoming, and 5 were found to be high school dropouts. Do these data indicate that the population proportion of high school dropouts on Oahu is different (either way) from that of Sweetwater County? Use a 1% level of significance. I need help with sketching, (d) and (e)
It is believed that 11% of all Americans are left-handed. A college needs to know how many left-handed desks to place in the big lecture halls being constructed on its campus. In a random sample of 210 students from that college, whether or not a student was left-handed was recorded for each student. The college wants to know if the data provide enough evidence to show that students at this college have a different percentage of left-handers than the general American population? State the random variable, population parameter, and hypotheses. State the Type I and Type II errors in the context of this problem.a) The symbol for the random variable involved in this problem is The wording for the random variable in context is as follows: b) The symbol for the parameter involved in this problem is The wording for the parameter in context is as follows: c) Fill in the correct null and alternative hypotheses: H0:H0: HA:HA:…
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?
Fifteen years ago, a complete survey of all undergraduate students at a large University indicated that the average student smoked 7.7 cigarettes per day. Th director of the student health center wishes to determine whether the incidence of cigarette smoking at his University has lessened over the fifteen year period. He obtains the following results (in cigarettes smoked per day) from a random sample of 9 students. 6.1, 9.2, 5, 6.3, 4.8, 3.2, 7.6, 8.1, 9. Test the null hypothesis at the .05 level significane.
It is believed that 11% of all Americans are left-handed. A college needs to know how many left-handed desks to place in the big lecture halls being constructed on its campus. In a random sample of 210 students from that college, whether or not a student was left-handed was recorded for each student. The college wants to know if the data provide enough evidence to show that students at this college have a higher percentage of left-handers than the general American population? State the random variable, population parameter, and hypotheses. State the Type I and Type II errors in the context of this problem.
It is believed that 11% of all Americans are left-handed. A college needs to know how many left-handed desks to place in the big lecture halls being constructed on its campus. In a random sample of 210 students from that college, whether or not a student was left-handed was recorded for each student. The college wants to know if the data provide enough evidence to show that students at this college have a higher percentage of left-handers than the general American population? State the random variable, population parameter, and hypotheses. State the Type I and Type II errors in the context of this problem.
It has been found that 25.1% of men (Group 1) 20 years and older suffer from hypertension (high blood pressure) and 33.9% of women (Group 2) are hypertensive. A random sample of 164 of each gender was selected from recent hospital records, and the following results were obtained. Can you conclude that a higher percentage of women have high blood pressure? Use =0.05. Men: 42 patients had high blood pressure Women: 52 patients had high blood pressure Required: Test Value Only the final answer should be rounded-off to TWO decimal places.
The Substance Abuse and Mental Health Services Administration (SAMHSA, 2017) estimates that 10.9% of the population of the United States age 18–24 had an episode of depression in the previous 12 months. Suppose a researcher takes a random sample of 225 United States adults aged 18–24. Determine the value of the sample proportion, p, such that 5% of samples of 225 United States adults age 18–24 are greater than p. You may find software or a z-table useful. Give your answer precise to three decimal places. p = II

SEE MORE QUESTIONS

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS