Questions and Answers of Fundamentals of Biostatistics

Answer Problem 6.12 for a 90% CI.Refer to the data in Table 2.13. Regard this hospital as typical of Pennsylvania hospitals.Table 2.13: Hospital-stay data
Compute a 95% CI for the mean white blood count following admission.Refer to the data in Table 2.13. Regard this hospital as typical of Pennsylvania hospitals.Table 2.13: Hospital-stay data
Compute a 95% CI for the mean age?Refer to the data in Table 2.13. Regard this hospital as typical of Pennsylvania hospitals.Table 2.13: Hospital-stay data
Answer Problem 6.2 for the list of treatment assignments derived in Problem 6.3?GastroenterologySuppose we are asked to construct a list of treatment assignments for patients entering a study
What is the standard error of the mean for each group?Pulmonary DiseaseThe data in Table 6.10 concern the mean triceps skin-fold thickness in a group of normal men and a group of men with chronic
Assume that the central-limit theorem is applicable. What does it mean in this context?Pulmonary DiseaseThe data in Table 6.10 concern the mean triceps skin-fold thickness in a group of normal men
Find the upper 1st percentile of a t distribution with 16 df?Pulmonary DiseaseThe data in Table 6.10 concern the mean triceps skin-fold thickness in a group of normal men and a group of men with
Find the lower 10th percentile of a t distribution with 28 df?Pulmonary DiseaseThe data in Table 6.10 concern the mean triceps skin-fold thickness in a group of normal men and a group of men with
Find the upper 2.5th percentile of a t distribution with 7 df?Pulmonary DiseaseThe data in Table 6.10 concern the mean triceps skin-fold thickness in a group of normal men and a group of men with
What are the upper and lower 2.5th percentiles for a chi-square distribution with 2 df? What notation is used to denote these percentiles? Pulmonary DiseaseThe data in Table 6.10 concern the
Suppose we change our minds and decide to enroll 40 patients and use four treatment groups. Use a computer program (such as MINITAB or Excel) to construct the list of random-treatment assignments
Count the number of people assigned to each treatment group. How does this number compare with the expected number in each group?GastroenterologySuppose we are asked to construct a list of treatment
Anticipating that 20 patients will be entered in the study and two treatments will be used, construct a list of random-treatment assignments starting in the 28th row of the random-number table (Table
What is the probability that the number of cardinal birds will be ≥ U at least once on Christmas day during the 10-year period 2012–2021?The observers wish to identify a normal range for the
If we make the same assumptions as in Problem 5.128, then what is L? What is U?The observers wish to identify a normal range for the number of cardinal birds observed per year. The normal range will
What is the probability of observing at least 60 cardinal birds in 2012? Suppose we assume that the distribution of the number of cardinal birds observed per year is normally distributed and that
What is the standard deviation (sd) of the number of cardinal birds observed?OrnithologyThe Christmas Bird Count (CBC) is an annual tradition in Lexington, Massachusetts. A group of volunteers counts
What is the mean number of cardinal birds per year observed from 2005 to 2011? OrnithologyThe Christmas Bird Count (CBC) is an annual tradition in Lexington, Massachusetts. A group of volunteers
Suppose we select a random 30- to 49-year-old Caucasian woman and a random 30- to 49-year-old African American woman. What is the probability that the African American woman has a higher true SBP?It
Suppose we want to observe the woman over n visits, where n is sufficiently large so that there is less than a 5% chance that her observed mean SBP will not differ from her true mean SBP by more than
Suppose a woman is measured at two visits with two readings per visit. If her true long-term SBP = 130 mm Hg, then what is the probability that her observed mean SBP is ≥140 mm Hg? (Ignore any
Are the data consistent with HWE? Specifically, is the number of heterozygotes (TC) significantly lower than expected under HWE? One issue is whether the Y402H gene is in Hardy-Weinberg
Under HWE, what is the expected frequency of the TC genotype among the 1185 subjects in the AMD = no group? One issue is whether the Y402H gene is in Hardy-Weinberg equilibrium (HWE). For a gene
What is the relative risk for AMD for the CC genotype compared with the TT genotype? Ophthalmology, GeneticsAge-related macular degeneration (AMD) is a common eye disease among the elderly that
If we assume that dropouts had the same distribution of change as the subjects in the control group, then what is the probability that an active subject who complied with the intervention lost
What is the probability that a random control group participant would lose at least 1 BMI unit over 24 months? In the control group of the Diabetes Prevention Trial, the mean change in BMI was 0
If the distribution of BMI change is approximately normal, then what is the probability that a subject in the active group would lose at least 1 BMI unit over 24 months? DiabetesThe Diabetes
What is the difference between a prevalence rate of breast cancer and an incidence rate of breast cancer? Another aspect of the study is to use the SWHS data to predict the long-term incidence
Suppose that in the year 2000 there are 10,000,000 Chinese women age 40 years with no prior breast cancer. What is the expected number of breast cancer cases in this group by the year 2025? (Assume
What is the predicted cumulative incidence of breast cancer from age 40 to 64 (i.e., over a 25-year period) among Chinese women? (Assume no deaths during this period.)Another aspect of the study is
Suppose the expected number of breast cancer cases among a large number of 45- to 49-year-old women in this study who were followed for 7 years is 149, while the observed number of cases is 107. Are
What is the probability that a woman has a low birth-weight delivery if she smokes during pregnancy? An important risk factor for low birth-weight delivery is maternal smoking during pregnancy
If 50 women are selected from the < 2500 g group, then what is the probability that at least half of them will have smoked during pregnancy? An important risk factor for low birth-weight
What is the probability that at least 2 women will have a low birth-weight delivery? ObstetricsA study was performed of different predictors of low birth-weight deliveries among 32,520 women in
If 20 women are randomly chosen from the study, what is the probability that exactly 2 will have a low birth-weight delivery (defined as < 2500 g)?ObstetricsA study was performed of different
What is z.90?The study is expanded to include 50 medical interns, of whom 11 report having had an automobile accident over the past year.One issue in the above study is that not all people report
What is the sum of the 40th and 60th percentiles of a normal distribution with a mean = 8.2 and variance = 9.5?The study is expanded to include 50 medical interns, of whom 11 report having had an
What is the 40th percentile of a normal distribution with mean = 5 and variance = 9? The study is expanded to include 50 medical interns, of whom 11 report having had an automobile accident over
Assess whether there is an excessive number of automobile accidents among interns under these altered assumptions? Explain your answer. The study is expanded to include 50 medical interns, of
What is an exact probability model for the number of automobile accidents over the past year for the 50 medical interns? (Note: The 11 reported accidents include both police-reported and
Apply the model in Problem 5.102 to assess whether there is an excessive number of automobile accidents among interns compared with the average 18- to 30-year old. Explain your answer?Accident
What is a reasonable probability model for the number of interns with at least one automobile accident over the past year? What are the parameters of this model? Accident EpidemiologyAutomobile
Does an unusual number of infants have at least one birth defect in the IVF group? Why or why not? PediatricsA study was recently published in Western Australia on the relationship between
How many infants with at least one birth defect would we expect among the 837 IVF infants if the true prevalence of at least one birth defect in the IVF group were the same as for infants conceived
What is the expected relative risk of macular degeneration for lutein-treated participants versus placebo-treated participants in the proposed study? Suppose for the sake of simplicity that the
What is the expected incidence rate of macular degeneration among lutein-treated participants?Suppose for the sake of simplicity that the incidence of macular degeneration is 1% per year among
Suppose that among people randomized to lutein tablets, at a 4-month follow-up the mean serum lutein level = 21 mg/dL with standard deviation = 8 mg/dL. If we presume a normal distribution for
Suppose that among people randomized to placebo, at a 4-month follow-up mean serum lutein level = 6.4 mg/dL with standard deviation = 3 mg/dL. If we presume a normal distribution for serum lutein,
Answer Problem 5.93 based on cases in winter?Researchers also analyzed cases occurring in the winter months. They found that on 10 days the pollution level on the index date was higher than on the
Given the preceding data, assess whether pollution level acts as a trigger effect in causing heart attack?Environmental HealthSome previous studies have shown that mortality rates are higher on days
Suppose the level of pollution has nothing to do with the incidence of heart attack. How many heart attacks would be expected to occur where the pollution level on the index date is higher than the
What is the probability that he is telling the truth? It is generally assumed that 75% of type-I diabetics comply with their insulin regimen. Suppose that a 12-year-old type-I diabetic boy comes
Answer the question in Problem 5.89 for non-compliant type-I diabetic 12-year-old boys?Conversely, 12-year-old type-I diabetic boys who do not take their insulin shots have a weight gain over 1 year
What is the probability that compliant type-I diabetic 12-year-old boys will gain at least 15 lbs. over 1 year? DiabetesPhysicians recommend that children with type-I (insulindependent) diabetes
If a 37-year-old RP patient has an initial total point score of 900 db and receives the implant treatment, what is the probability that the patient will become legally blind by age 50? Suppose a
If a 37-year-old RP patient has an initial total point score of 900 db, what is the probability that the patient will become legally blind (that is, have a total point score of < 250 db) by age
What is the probability that a patient will change by ≥ 200 db over 5 years? OphthalmologyRetinitis pigmentosa (RP) is a genetic ocular disease that results in substantial visual loss and in
Do you think the distribution of FAIR test scores within a group is normally distributed? Why or why not?OrthopedicsA study was conducted of a diagnostic test (the FAIR test, i.e., hip flexion,
The criterion of ≥ 1.86 ms to define a positive test is arbitrary. Using different cutoff points to define positivity, obtain the ROC curve for the FAIR test. What is the area under the ROC curve?
Suppose that 70% of the participants who are referred to an orthopedist who specializes in PS will actually have the condition. If a test score of ≥ 1.86 ms is obtained for a participant, then what
What is the specificity of the test for this cutoff point?OrthopedicsA study was conducted of a diagnostic test (the FAIR test, i.e., hip flexion, adduction, and internal rotation) used to identify
What is the sensitivity of the test for this cutoff point?OrthopedicsA study was conducted of a diagnostic test (the FAIR test, i.e., hip flexion, adduction, and internal rotation) used to identify
Perform a simulation of this process (e.g., using MINITAB, Excel, or R) with 100 balls, and plot the frequency distribution of the position of the balls at the bottom with respect to the entry
Can you think of an approximation to the distribution derived in Problem 5.78? SIMULATIONAn apparatus displaces a collection of balls to the top of a stack by suction. At the top level (Level 1)
What is the exact probability distribution of the position of the balls at the bottom with respect to the entry position (arbitrarily denoted by 0)? SIMULATIONAn apparatus displaces a collection
1. Draw 100 random samples from a binomial distribution with parameters n = 10 and p = .4. Consider an approximation to this distribution by a normal distribution with mean = np = 4 and variance =
What percentage of hypertension at age 50 is attributable to the weight gain from age 18 to 50?Cardiovascular DiseaseObesity is an important determinant of cardiovascular disease because it directly
If the standard deviation of SBP under the assumption in Problem 5.72 remained the same (15 mm Hg), and the distribution of SBP remained normal, then what would be the expected proportion of
Suppose an average woman did not gain any weight from age 18 to 50. What average SBP for 50-year-old women would be expected under these assumptions? Cardiovascular DiseaseObesity is an
Consider the nutrients saturated fat, total fat, and total calories. Plot the distribution of each nutrient for both the diet record and the food-frequency questionnaire. Do you think a normal
Answer Problem 5.59 using the ln(nutrient) transformation for each nutrient value. Is the normality assumption more appropriate for log-transformed or un-transformed values, or neither?
A special problem arises for the nutrient alcohol consumption. There are often a large number of nondrinkers (alcohol consumption = 0) and another large group of drinkers (alcohol consumption >
Among cystic-fibrosis patients, 37 cancers were observed, whereas 45.6 cancers were expected. What distribution can be used to model the distribution of the number of cancers among cystic-fibrosis
Are there an unusually low number of cancers among cystic-fibrosis patients?Cancer, NeurologyA study concerned the risk of cancer among patients with cystic fibrosis [5]. Given registries of patients
In the same study 13 cancers of the digestive tract were observed, whereas only 2 cancers were expected. Are there an unusually high number of digestive cancers among cystic-fibrosis patients?Cancer,
If we assume the change in mean DBP is normally distributed, then what is the probability that a subject will decline by at least 5 mm Hg if 1 replicate measure is obtained at baseline and
The physician also knows that if a patient is untreated (or does not take the prescribed medication), then the mean DBP over 4 weeks will decline by 2 mm Hg with variance 33/n. What is the
Suppose the physician is not sure whether the patient is actually taking the prescribed medication. She wants to take enough replicate measurements at baseline and follow-up so that the probability
If a decline of 2% in bone-mineral density is considered clinically significant, then what percentage of women in the placebo group can be expected to show a decline of at least this
What percentage of women in the alendronate 5-mg group can be expected to have a clinically significant decline in bone-mineral density as defined in Problem 5.68? The change in bone-mineral
Suppose 10% of the women assigned to the alendronate 5-mg group are actually not taking their pills (noncompliers). If noncompliers are assumed to have a similar response as women in the placebo
What proportion of 50-year-old women is hypertensive, if hypertension is defined as SBP ≥ 140 mm Hg?Cardiovascular DiseaseObesity is an important determinant of cardiovascular disease because it
A study was conducted relating particulate air pollution and daily mortality in Steubenville, Ohio [4]. On average over the past 10 years there have been 3 deaths per day in Steubenville. Suppose
Based on the results in Problem 5.56, should the program be implemented? Why or why not?The program will be implemented if at least 50% of the GDM women in the program are no more than 2 lbs. above
What % of the GDM women in the program will be expected to be no more than 2 lbs. above their pre-pregnancy weight? Officials in the State Health Department are considering using the active
What are the approximate 10th and 90th percentiles of weight change from pre-pregnancy to 12 months postpartum among women in the active group? Among women in the control group?At 12 months
What is the probability that a control group woman was at or below her pre-pregnancy weight at 12 months?At 12 months postpartum, women in the control group gained a mean of 7.9 lbs. with a standard
If we assume that the change in weight from prepregnancy to 12 months is normally distributed, then what percent of women in the active group were at or below their pre-pregnancy weight at 12 months
What is the smallest number of hepatomas that would have to be observed among the alcoholics with cirrhosis of the liver for the hepatoma experience in this group to differ from the hepatoma
What is the probability of observing at least 29 hepatomas among the 84 alcoholics with cirrhosis of the liver under the assumptions in Problem 5.50?Hepatic DiseaseSuppose we observe 84 alcoholics
What is the probability that we observe exactly 29 alcoholics with cirrhosis of the liver who have hepatomas if the true rate of hepatoma among alcoholics (with or without cirrhosis of the liver) is
The distribution of plasma-aldosterone concentration in 53 Caucasian and 46 African American children is shown in Figure 5.22. Does the assumption of normality seem reasonable? Why or why not?Figure
If the mean plasma-aldosterone level in Caucasian children is 400 pmol/L with standard deviation of 218 pmol/L, then what percentage of Caucasian children have levels ≤ 300 pmol/L if normality is
If the mean plasma-aldosterone level in African American children was 230 pmol/L with a standard deviation of 203 pmol/L, then what percentage of African American children have levels ≤ 300 pmol/L
1. Describe the effect of each treatment regimen on changes in heart rate and blood pressure. Does the distribution of changes in these parameters look normal or not?2. Compare graphically the
Repeat the analyses in Problem 5.43 separately for boys and girls. Are your conclusions the same in the two groups?
Repeat the analyses in Problem 5.42 for the subgroup of children 10+ years of age (because smoking is very rare before this age). Do you reach similar conclusions? Data from 5.42Plot the
Plot the distribution of z-scores for smokers and nonsmokers separately. Do these distributions look normal? Do smoking and pulmonary function seem in any way related in these data?
Suppose we consider the serum vitamin E assay as a screening test for compliance with vitamin E supplementation. Participants whose change in serum vitamin E is ‰¥ Î” mg/dL will
Suppose a new threshold of change, Î” mg/dL, is proposed for establishing compliance. We wish to use a level of Î” such that the compliance measures in Problems 5.36 and 5.38

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