Fundamentals of Biostatistics
8th Edition
ISBN: 9781305268920
Author: Bernard Rosner
Publisher: Cengage Learning
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Textbook Question
Chapter 4, Problem 48P
An important issue in assessing nuclear energy is whether excess disease risks exist in the communities surrounding nuclear-power plants. A study undertaken in the community surrounding Hanford, Washington, looked at the prevalence of selected congenital malformations in the counties surrounding the nuclear-test facility [9].
Suppose 27 cases of Down’s syndrome are found and only 19 are expected based on Birth Defects Monitoring Program prevalence estimates in the states of Washington, Idaho, and Oregon. Are there significant excess cases in the area around the nuclear-power plant?
Suppose 12 cases of cleft palate are observed, whereas only 7 are expected based on Birth Defects Monitoring Program estimates.
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Cycles to
failure
Position in
ascending
order
0.5
f(x))
(x;)
Problem 44
Marsha, a renowned cake scientist, is trying to determine how long different cakes can survive intense fork attacks before collapsing into crumbs.
To simulate real-world cake consumption, she designs a test where cakes are subjected to repeated fork stabs and bites, mimicking the brutal
reality of birthday parties. After rigorous testing, Marsha records 10 observations of how many stabs each cake endured before structural failure.
Construct P-P plots for (a.) a normal distribution, (b.) a lognormal distribution, and (c.) a Weibull distribution (using the information included in the
table below). Which distribution seems to be the best model for the cycles to failure for this material? Explain your answer in detail.
Observation
Empirical
cumulative
Probability distribution
Cumulative distribution
Inverse of cumulative
distribution F-1 (-0.5)
F(x))
(S)
n
4
3
1
0.05
9
5
2
0.15
7
7
3
0.25
1
10
4
0.35
3
12
5
0.45
Normal…
Problem 3
In their lab, engineer Daniel and Paulina are desperately trying to perfect time travel. But the problem is that
their machine still struggles with power inconsistencies-sometimes generating too little energy, other times
too much, causing unstable time jumps. To prevent catastrophic misjumps into the Jurassic era or the far
future, they must calibrate the machine's power output. After extensive testing, they found that the time
machine's power output follows a normal distribution, with an average energy level of 8.7 gigawatts and a
standard deviation of 1.2 gigawatts.
The Time Travel Safety Board has set strict guidelines: For a successful time jump, the
machine's power must be between 8.5 and 9.5 gigawatts. What is the probability that a randomly
selected time jump meets this precision requirement?
Daniel suggests that adjusting the mean power output could improve time-travel accuracy.
Can adjusting the mean reduce the number of dangerous misjumps? If yes, what should the…
Problem 5 (
Marybeth is also interested in the experiment from Problem 2 (associated with the enhancements for Captain
America's shield), so she decides to start a detailed literature review on the subject. Among others, she found
a paper where they used a 2"(4-1) fractional factorial design in the factors: (A) shield material, (B) throwing
mechanism, (C) edge modification, and (D) handle adjustment. The experimental design used in the paper is
shown in the table below.
a.
Run
A
B
с
D
1
(1)
-1
-1
-1
1
2
a
1
-1
-1
1
3
bd
-1
1
-1
1
4
abd
1
1
-1
1
5
cd
-1
-1
1
-1
6
acd
1
-1
1
-1
7
bc
-1
1
1
-1
abc
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paper?
s) What was the generator used in the 2"(4-1) fractional factorial design described in the
b.
Based on the resolution of this design, what do you think about the generator used in the
paper? Do you think it was a good choice, or would you have selected a different one? Explain your
answer in detail.
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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