Questions and Answers of Fundamentals of Biostatistics

Is the measure in Problem 5.38 a measure of sensitivity, specificity, or predictive value?CancerA treatment trial is proposed to test the efficacy of vitamin E as a preventive agent for cancer. One
What percentage of the placebo group would be expected to show a change of not more than 0.30 mg/dL?CancerA treatment trial is proposed to test the efficacy of vitamin E as a preventive agent for
Is the measure in Problem 5.36 a measure of sensitivity, specificity, or predictive value? CancerA treatment trial is proposed to test the efficacy of vitamin E as a preventive agent for cancer.
Suppose a change of 0.30 mg/dL in serum levels is proposed as a test criterion for compliance; that is, a patient who shows a change of ‰¥ 0.30 mg/dL is considered a compliant vitamin E
Suppose that in a pharmacologic study involving 6000 patients, 75 patients have blood-glucose levels at least 1.5 times the upper limit of normal on one occasion. What is the probability that this
Frequently, tests that yield abnormal results are repeated for confirmation. What is the probability that for a normal person a test will be at least 1.5 times as high as the upper limit of normal on
Answer Problem 5.32 for values 2.0 times the upper limit of normal?Blood ChemistryIn pharmacologic research a variety of clinical chemistry measurements are routinely monitored closely for evidence
In some studies only values at least 1.5 times as high as the upper limit of normal are identified as abnormal. What percentage of values would fall in this range?Blood ChemistryIn pharmacologic
If the normal range is 65−120 mg/dL, then what percentage of values will fall in the normal range?Blood ChemistryIn pharmacologic research a variety of clinical chemistry measurements are routinely
How large would x have to be for the probability of a normal adult having x or more neutrophils to be ≤1%?Infectious DiseaseThe differential is a standard measurement made during a blood test. It
An excess of neutrophils is consistent with several types of bacterial infection. Suppose an adult has x neutrophils. How large would x have to be for the probability of a normal adult having x or
How many lymphocytes would have to appear in the differential before you would feel the “normal” pattern was violated? Infectious DiseaseThe differential is a standard measurement made
What is the probability a normal adult will have 50 or more lymphocytes? Infectious DiseaseThe differential is a standard measurement made during a blood test. It consists of classifying white
An excess of lymphocytes is consistent with various forms of viral infection, such as hepatitis. What is the probability that a normal adult will have 40 or more lymphocytes? Infectious
An excess of eosinophils is sometimes consistent with a violent allergic reaction. What is the exact probability that a normal adult will have 5 or more eosinophils?Infectious DiseaseThe differential
Answer Problem 5.23 for a 25-year-old man with an FEV of 4.0 L?Pulmonary DiseaseForced expiratory volume (FEV) is an index of pulmonary function that measures the volume of air expelled after 1
What is the probability that a 45-year-old man with an FEV of 4.0 L will be functionally impaired by age 75? Pulmonary DiseaseForced expiratory volume (FEV) is an index of pulmonary function
Answer Problem 5.21 for a nonsmoking man?Some people are not functionally impaired now, but their pulmonary function usually declines with age and they eventually will be functionally impaired.
If an FEV of less than 2.5 L is regarded as showing some functional impairment (occasional breathlessness, inability to climb stairs, etc.), then what is the probability that a currently smoking man
What proportion of 15- to 44-year-olds are hypertensive? HypertensionPeople are classified as hypertensive if their systolic blood pressure (SBP) is higher than a specified level for their age
What proportion of families are hypertensive? (Assume that the hypertensive status of different members of a family are independent random variables.)HypertensionPeople are classified as hypertensive
Suppose a community has 1000 families living in it. What is the probability that between one and five families are hypertensive?HypertensionPeople are classified as hypertensive if their systolic
What proportion of 1- to 14-year-olds are hypertensive?HypertensionPeople are classified as hypertensive if their systolic blood pressure (SBP) is higher than a specified level for their age group,
What proportion of the general population has borderline high-cholesterol levels—that is, > 200 but < 250 mg/dL? Cardiovascular DiseaseSerum cholesterol is an important risk factor for
Some investigators believe that only cholesterol levels over 250 mg/dL indicate a high-enough risk for heart disease to warrant treatment. What proportion of the population does this group
If the clinically desirable range for cholesterol is < 200 mg/dL, what proportion of people have clinically desirable levels of cholesterol? Cardiovascular Disease, Pulmonary DiseaseThe
Answer Problem 5.12 for women?Cardiovascular Disease, Pulmonary DiseaseThe duration of cigarette smoking has been linked to many diseases, including lung cancer and various forms of heart disease.
Assuming that the duration of smoking is normally distributed, what proportion of men in this age group have smoked for more than 20 years? Cardiovascular Disease, Pulmonary DiseaseThe duration
If we assume that the distribution of Δ is normally distributed, then what is the 90 percentile (i.e., the upper decile) and 10 percentile (i.e., the lower decile) of the distribution?HypertensionA
If we assume that the distribution of Δ is normally distributed, then what % of (observer, trainer) pairs have a mean difference of ≥ 2 mm Hg in absolute value (i.e., either ≥ 2 mm Hg or ≤
Answer Problem 5.7 for boys in this age range and economic environment?Suppose boys in this age range who live below the poverty level have a mean carbohydrate intake of 121 g/1000 cal with a
Answer Problem 5.6 for boys in this age range and economic environment?Suppose boys in this age range who live below the poverty level have a mean carbohydrate intake of 121 g/1000 cal with a
What percentage of boys in this age range have carbohydrate intake below 90 g/1000 cal?NutritionSuppose that total carbohydrate intake in 12- to 14-year old boys is normally distributed, with mean =
What percentage of boys in this age range have carbohydrate intake above 140 g/1000 cal?NutritionSuppose that total carbohydrate intake in 12- to 14-year old boys is normally distributed, with mean =
What proportion of people have borderline cholesterol? Suppose a person is regarded as having high cholesterol if Z > 2.0 and borderline cholesterol if 1.5 < Z < 2.0.
What proportion of people have high cholesterol?Suppose a person is regarded as having high cholesterol if Z > 2.0 and borderline cholesterol if 1.5 < Z < 2.0.
What is Pr(−1.0 < Z < 1.5)?Cardiovascular DiseaseBecause serum cholesterol is related to age and sex, some investigators prefer to express it in terms of z-scores. If X = raw serum
What is Pr(Z > 0.5)?Cardiovascular DiseaseBecause serum cholesterol is related to age and sex, some investigators prefer to express it in terms of z-scores. If X = raw serum cholesterol, then Z =
What is Pr(Z < 0.5)? Cardiovascular DiseaseBecause serum cholesterol is related to age and sex, some investigators prefer to express it in terms of z-scores. If X = raw serum cholesterol,
1. Answer Problem 4.74 for bone density of the femoral neck?2. Answer Problem 4.75 for bone density of the femoral neck?
The cutoff of 18 months is arbitrary. ln a larger study, the investigator wants to use a cutoff (x) so that the probability of surviving for at least x months is < 1%, if the treatment has no
The surgeon is encouraged by the result and tries the treatment on 5 other patients. He finds that 3 of the 5 patients survive for at least 18 months. What is the probability that at least 3 of 5
A surgeon tries an experimental treatment on 1 patient, and the patient survives for 18 months. lf we assume the distribution of survival time is Poisson-distributed, then what is the probability
Suppose we have 10 patients who receive lnterleukin- 2 plus vaccine of whom 2 develop arrhythmia and 8 do not. What is the probability that exactly 3 of the 10 patients will get a positive response
lf 20 melanoma patients are given lnterleukin-2 plus a vaccine, what is the probability that at least 3 of them will have a positive response to treatment?CancerA clinical trial was conducted among
lf 20 melanoma patients are given lnterleukin-2 plus a vaccine, what is the probability that exactly 5 of them will have a positive response to treatment (either complete or partial response)?CancerA
Suppose 1000 potential participants are contacted to participate in the survey. What is the probability that at least 10 of the 1000 participants will be eligible and agree to
Suppose the survey is given to 100 subjects. What is the probability of obtaining at least 2 eligible responders who agree to participate?EpidemiologyA study was performed to assess the feasibility
Calculate the probability that a flight attendant encounters at least one DIV over his/her 20-year working lifetlme. Make the same assumptions as in Problem 4.96.Emergency MedicineA study was
Suppose the flight attendant’s total duration of employment is 20 years. What is the probability that he/she encounters at least 10 IFMs on his/her flights over a 20-year period? Make the same
Suppose a flight attendant works on 2 flights per day for each of 300 days per year. What is the probability that the flight attendant will encounter at least one IFM over a 1-year period?Emergency
What is the expected number of cases over 1 year in the city?Suppose a city is divided into eight census tracts as shown in Table 4.21.Table 4.21: Relationship between incidence of birth defects and
Suppose a child is born with the birth defect but the address of the mother is unknown. What is the probability that the child comes from a low SES census tract?Suppose a city is divided into eight
If there are 5000 births in the census tract in 1 year, then what is the probability that there will be exactly 5 cases of the birth defect during the year (census tract A in Table 4.21)?Table 4.21:
If there are 12,000 births in the census tract in 1 year, then what is the probability that there will be at least 8 cases of the birth defect during the year (census tract B in Table 4.21)?Table
What is the probability of having 0, 1, and 2+ admissions for an entire week, if the results for different days during the week are assumed to be independent?Hospital EpidemiologySuppose the number
What is the probability of at least one admission on a Saturday?Hospital EpidemiologySuppose the number of admissions to the emergency room at a small hospital follows a Poisson distribution but the
What is the probability of at least one admission on a Wednesday?Hospital EpidemiologySuppose the number of admissions to the emergency room at a small hospital follows a Poisson distribution but the
Suppose dental practice improves over the 30-year period. We assume the rate of tooth loss per year from 1987−2001 (15 years) is the same as in 1987, whereas the rate of tooth loss per year from
Suppose that on January 1, 1987, a man is 50 years old, that he will live for 30 more years (until 2016), and that the rate of tooth loss over this 30-year period is the same as in 1987. If a man has
If we assume the average number of teeth lost in the 5−9 group is 7 teeth and the average number of teeth lost in the 10+ group is 12 teeth, what is the best estimate of the average number of teeth
Suppose a woman has 300 intermediate cells by age 45. What is the probability that she develops breast cancer by age 46? By age 50?CancerThe two-stage model of carcinogenesis is based on the premise
What is the expected number of intermediate cells by age 45?The probability that an intermediate cell will mutate to become a malignant cell is 5 × 10−7 per year.CancerThe two-stage model of
What is the probability that there will be at least 5 intermediate cells by age 21?CancerThe two-stage model of carcinogenesis is based on the premise that for a cancer to develop, a normal cell must
Answer Problem 4.80 for a binomial distribution with parameters n = 10 and p = .5. Compare your results with Figure 4.5(c).Figure 4.5(c):(c) n = 10, p = .50SIMULATIONAn attractive feature of modern
Answer Problem 4.80 for a binomial distribution with parameters n = 10 and p = .95. Compare your results with Figure 4.5(b).Figure 4.5(b):(b) n = 10, p = .95SIMULATIONAn attractive feature of modern
Draw 100 random samples from a binomial distribution, each based on 10 trials with probability of success = .05 on each trial. Obtain a frequency distribution of the number of successes over the 100
1. Consider the Data Set BONEDEN.DAT at www.cengagebrain.com. Calculate the difference in bone density of the lumbar spine (g/cm2) between the heavier-smoking twin and the lighter-smoking twin (bone
Does the abortion rate among nurses differ significantly from the national experience? Why or why not?Studies have been undertaken to assess the relationship between abortion and the development of
What is the expected number of abortions among nurses over this time period if the incidence of abortion is 25 per 1000 women per year and no woman has more than 1 abortion?Studies have been
If we assume (1) no woman has more than 1 abortion and (2) the probability of having an abortion is independent across different years, what is the probability that a 15-year old woman in 1975 will
Answer Problem 4.67 for a random day during the year?Environmental HealthSome previous studies have shown a relationship between emergency-room admissions per day and level of pollution on a given
On a random day during the year, what is the probability there will be 4 admissions to the emergency ward, assuming there are 345 normal-pollution days and 20 high-pollution days?Environmental
The hospital also finds that on high-pollution days the number of admissions is Poisson-distributed with mean = 4.0 admissions per day. Answer Problem 4.67 for high pollution days?Environmental
The hospital is planning a new emergency-room facility. It wants enough beds in the emergency ward so that for at least 95% of normal-pollution days it will not need to turn anyone away. What is the
What is the maximum number of cardiac deaths that could have occurred on the day of the earthquake to be consistent with the rate of cardiac deaths in the past week?Cardiovascular DiseaseAn article
Is the occurrence of 51 deaths unusual?Cardiovascular DiseaseAn article was published [13] concerning the incidence of cardiac death attributable to the earthquake in Los Angeles County on January
What is the exact probability of 51 deaths occurring on one day if the cardiac death rate in the previous week continued to hold on the day of the earthquake?Cardiovascular DiseaseAn article was
What does cumulative incidence mean, in words, in the context of this problem?Ophthalmology, DiabetesA study [12] of incidence rates of blindness among insulindependent diabetics reported that the
After how many years of follow-up would we expect the cumulative incidence of blindness to be 10% among 30-year-old IDDM females, if the incidence rate remains constant over time?Ophthalmology,
What is the probability that a 30-year-old IDDM male patient will go blind over the next 10 years?Ophthalmology, DiabetesA study [12] of incidence rates of blindness among insulindependent diabetics
If a group of 200 IDDM 30- to 39-year-old women is followed, what is the probability that at least 2 will go blind over a 1-year period?Ophthalmology, DiabetesA study [12] of incidence rates of
If a group of 200 IDDM 30- to 39-year-old men is followed, what is the probability that exactly 2 will go blind over a 1-year period?Ophthalmology, DiabetesA study [12] of incidence rates of
Is the distribution of the number of HIV positive among the 20 users binomial? Why or why not?Infectious DiseaseA study considered risk factors for HIV infection among intravenous drug users [11]. It
What is the probability that at least 4 of the 20 users are HIV positive?Infectious DiseaseA study considered risk factors for HIV infection among intravenous drug users [11]. It found that 40% of
Suppose we have a group of 10 light users and 10 heavy users. What is the probability that exactly 3 of the 20 users are HIV positive?Infectious DiseaseA study considered risk factors for HIV
What is the probability that at least 3 of 5 light users are HIV positive?Infectious DiseaseA study considered risk factors for HIV infection among intravenous drug users [11]. It found that 40% of
What is the probability that exactly 3 of 5 light users are HIV positive?Infectious DiseaseA study considered risk factors for HIV infection among intravenous drug users [11]. It found that 40% of
A topic of some interest in the genetic literature over at least the past 30 years has been the study of sexratio data. In particular, one suggested hypothesis is that there are enough families with
Develop life tables for subsets of the data based on age, gender, number of cigarettes per day, and CO level (one variable at a time). Given these data, do you feel age, gender, number of cigarettes
Develop a life table similar to Table 4.16, giving the number of people who remained abstinent at 1, 2, . . . , 12 months of life (assume for simplicity that there are 30 days in each of the first 11
Do you feel there is a meaningful excess number of cases of cleft palate in the area surrounding the nuclear power plant? Explain.Suppose 12 cases of cleft palate are observed, whereas only 7 are
What is the probability of observing exactly 12 cases of cleft palate if there is no excess risk of cleft palate in the study area?Suppose 12 cases of cleft palate are observed, whereas only 7 are
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
Can you write a general formula for the probability that x rats will die in the 8-hour period? Evaluate this formula for x = 0, 1, . . . , 10.Cancer, EpidemiologyAn experiment is designed to test the
What is the probability that 2 rats will die in the 8-hour period?Cancer, EpidemiologyAn experiment is designed to test the potency of a drug on 20 rats. Previous animal studies have shown that a
What is the probability that 1 rat will die in the 8-hour period?Cancer, EpidemiologyAn experiment is designed to test the potency of a drug on 20 rats. Previous animal studies have shown that a
What is the probability that 0 rats will die in the 8-hour period?Cancer, EpidemiologyAn experiment is designed to test the potency of a drug on 20 rats. Previous animal studies have shown that a
Suppose 2 rats die in the first 4 hours. What is the probability that 2 or fewer rats will die in the next 4 hours?Cancer, EpidemiologyAn experiment is designed to test the potency of a drug on 20
What is the probability that 3 or more rats will die in the first 4 hours?Cancer, EpidemiologyAn experiment is designed to test the potency of a drug on 20 rats. Previous animal studies have shown

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