
Fundamentals of Biostatistics
8th Edition
ISBN: 9781305268920
Author: Bernard Rosner
Publisher: Cengage Learning
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Textbook Question
Chapter 4, Problem 4P
Let X be the random variable representing the number of hypertensive adults in Example 3.12.
What is its cumulative-distribution
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3. Bayesian Inference – Updating Beliefs
A medical test for a rare disease has the following characteristics:
Sensitivity (true positive rate): 99%
Specificity (true negative rate): 98%
The disease occurs in 0.5% of the population.
A patient receives a positive test result.
Questions:
a) Define the relevant events and use Bayes’ Theorem to compute the probability that the patient actually has the disease.b) Explain why the result might seem counterintuitive, despite the high sensitivity and specificity.c) Discuss how prior probabilities influence posterior beliefs in Bayesian inference.d) Suppose a second, independent test with the same accuracy is conducted and is also positive. Update the probability that the patient has the disease.
4. Linear Regression - Model Assumptions and Interpretation
A real estate analyst is studying how house prices (Y) are related to house size in square feet (X). A simple
linear regression model is proposed:
The analyst fits the model and obtains:
•
Ŷ50,000+150X
YBoB₁X + €
•
R² = 0.76
• Residuals show a fan-shaped pattern when plotted against fitted values.
Questions:
a) Interpret the slope coefficient in context.
b) Explain what the R² value tells us about the model's performance.
c) Based on the residual pattern, what regression assumption is likely violated? What might be the
consequence?
d) Suggest at least two remedies to improve the model, based on the residual analysis.
5. Probability Distributions – Continuous Random Variables
A factory machine produces metal rods whose lengths (in cm) follow a continuous uniform distribution on the interval [98, 102].
Questions:
a) Define the probability density function (PDF) of the rod length.b) Calculate the probability that a randomly selected rod is shorter than 99 cm.c) Determine the expected value and variance of rod lengths.d) If a sample of 25 rods is selected, what is the probability that their average length is between 99.5 cm and 100.5 cm? Justify your answer using the appropriate distribution.
Chapter 4 Solutions
Fundamentals of Biostatistics
Ch. 4.6 - What is the difference between a frequency...Ch. 4.6 - What is the difference between a probability-mass...Ch. 4.6 - In Table 4.4 the random variable X represents the...Ch. 4.7 - Suppose we select 3 students randomly out of a...Ch. 4.7 - Suppose we select 2 students randomly from a class...Ch. 4.9 - The probability of a woman developing breast...Ch. 4.9 - Suppose we have 10 subjects and the probability of...Ch. 4.13 - Suppose the number of motor-vehicle fatalities in...Ch. 4.13 - Suppose a rare infectious disease occurs at the...Ch. 4 - Let X be the random variable representing the...
Ch. 4 - Let X be the random variable representing the...Ch. 4 - Let X be the random variable representing the...Ch. 4 - Let X be the random variable representing the...Ch. 4 - Suppose we want to check the accuracy of...Ch. 4 - Suppose we want to check the accuracy of...Ch. 4 - Evaluate (100),(101),,(1010).Ch. 4 - Evaluate 9!.Ch. 4 - Suppose 6 of 15 students in a grade-school class...Ch. 4 - What is the expected number of students in the...Ch. 4 - What is the probability of obtaining exactly 6...Ch. 4 - What is the probability of obtaining at least 6...Ch. 4 - What is the expected value and variance for a...Ch. 4 - Prob. 14PCh. 4 - Infectious Disease Newborns were screened for...Ch. 4 - Infectious Disease Newborns were screened for...Ch. 4 - Infectious Disease Newborns were screened for...Ch. 4 - Infectious Disease Newborns were screened for...Ch. 4 - Prob. 19PCh. 4 - Infectious Disease Newborns were screened for...Ch. 4 - Infectious Disease Newborns were screened for...Ch. 4 - Infectious Disease Newborns were screened for...Ch. 4 - Suppose 10 gonorrhea cases are reported over a...Ch. 4 - Assume the number of episodes per year of otitis...Ch. 4 - Assume the number of episodes per year of otitis...Ch. 4 - An interesting question in pediatrics is whether...Ch. 4 - What is the probability that exactly 1 sibling...Ch. 4 - An interesting question in pediatrics is whether...Ch. 4 - What is the expected number of siblings in a...Ch. 4 - A national study found that treating people...Ch. 4 - A national study found that treating people...Ch. 4 - A national study found that treating people...Ch. 4 - The presence of bacteria in a urine sample...Ch. 4 - The presence of bacteria in a urine sample...Ch. 4 - The presence of bacteria in a urine sample...Ch. 4 - One interesting phenomenon of bacteriuria is that...Ch. 4 - One interesting phenomenon of bacteriuria is that...Ch. 4 - Otitis media is a disease that occurs frequently...Ch. 4 - Otitis media is a disease that occurs frequently...Ch. 4 - Otitis media is a disease that occurs frequently...Ch. 4 - Otitis media is a disease that occurs frequently...Ch. 4 - An experiment is designed to test the potency of a...Ch. 4 - An experiment is designed to test the potency of a...Ch. 4 - An experiment is designed to test the potency of a...Ch. 4 - An experiment is designed to test the potency of a...Ch. 4 - An experiment is designed to test the potency of a...Ch. 4 - An experiment is designed to test the potency of a...Ch. 4 - An important issue in assessing nuclear energy is...Ch. 4 - Prob. 49PCh. 4 - An important issue in assessing nuclear energy is...Ch. 4 - Prob. 51PCh. 4 - Prob. 52PCh. 4 - A topic of some interest in the genetic literature...Ch. 4 - A study considered risk factors for HIV infection...Ch. 4 - A study considered risk factors for HIV infection...Ch. 4 - A study considered risk factors for HIV infection...Ch. 4 - A study considered risk factors for HIV infection...Ch. 4 - A study considered risk factors for HIV infection...Ch. 4 - A study [12] of incidence rates of blindness among...Ch. 4 - A study [12] of incidence rates of blindness among...Ch. 4 - A study [12] of incidence rates of blindness among...Ch. 4 - A study [12] of incidence rates of blindness among...Ch. 4 - A study [12] of incidence rates of blindness among...Ch. 4 - An article was published [13] concerning the...Ch. 4 - An article was published [13] concerning the...Ch. 4 - An article was published [13] concerning the...Ch. 4 - Some previous studies have shown a relationship...Ch. 4 - Some previous studies have shown a relationship...Ch. 4 - Some previous studies have shown a relationship...Ch. 4 - Some previous studies have shown a relationship...Ch. 4 - The number of legal induced abortions per year per...Ch. 4 - Table 4.19 Annual incidence of legal induced...Ch. 4 - Some previous studies have shown a relationship...Ch. 4 - Prob. 80PCh. 4 - Prob. 81PCh. 4 - Prob. 82PCh. 4 - The two-stage model of carcinogenesis is based on...Ch. 4 - The two-stage model of carcinogenesis is based on...Ch. 4 - The two-stage model of carcinogenesis is based on...Ch. 4 - The data in Table 4.20 were reported by men in the...Ch. 4 - The data in Table 4.20 were reported by men in the...Ch. 4 - Prob. 88PCh. 4 - Suppose the number of admissions to the emergency...Ch. 4 - Suppose the number of admissions to the emergency...Ch. 4 - Suppose the number of admissions to the emergency...Ch. 4 - Prob. 92PCh. 4 - Prob. 93PCh. 4 - Prob. 94PCh. 4 - Suppose a city is divided into eight census tracts...Ch. 4 - A study was performed concerning medical...Ch. 4 - Suppose the flight attendants total duration of...Ch. 4 - The more significant IFMs result in an aircraft...Ch. 4 - A study was performed to assess the feasibility of...Ch. 4 - A study was performed to assess the feasibility of...Ch. 4 - A clinical trial was conducted among 178 patients...Ch. 4 - Prob. 102PCh. 4 - Suppose we have 10 patients who receive...Ch. 4 - Mesothelioma is an asbestos-related neoplasm that...Ch. 4 - Mesothelioma is an asbestos-related neoplasm that...Ch. 4 - Mesothelioma is an asbestos-related neoplasm that...
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