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mathematics
fundamentals of biostatistics
Questions and Answers of
Fundamentals of Biostatistics
Perform the procedure mentioned in Problem 7.101, and report a two-tailed p-value?OphthalmologyA study was performed among patients with glaucoma, an important eye disease usually manifested by high
What procedure can be used to test the hypothesis that there has been no mean difference in IOP after 60 days Data set available between the two drug regimens? OphthalmologyA study was performed
What would be the power of the type of test used in Problem 7.99 under these assumptions? Suppose the true effect of the intervention is to reduce the number of medical errors per day by 20% (to
Implement the test in Problem 7.98, and report a two-tailed p-value?Hospital EpidemiologyMedical errors are common in hospitals throughout the world. One possible causal factor is the long work hours
What test can be used to test the hypothesis that an increase in amount of sleep will change the number of medical errors per day? Hospital EpidemiologyMedical errors are common in hospitals
Does the effect of the placebo eye drop change over time after drop instillation? Compare mean TBUT at 5, 10, and 15 minutes postinstillation vs. mean TBUT immediately after drop instillation.
Is there an immediate effect of the eye drop on TBUT?
Provide a 95% CI for the underlying fetal death rate among offspring of exposed men. Given the CI, how do you interpret the results of the study? Another type of outcome reported was fetal
Implement the test in Problem 7.93, and report a p-value (two-tailed)?Environmental Health, Pulmonary DiseaseA clinical epidemiologic study was conducted to determine the long-term health effects of
What hypothesis test can be used to test the hypothesis that the percentage of abnormal FEV values among exposed men differs from the general-population estimates? Environmental Health,
Suppose the case-fatality rate from neuroblastoma is usually 1/6. Furthermore, 17 fatal cases occurred among the 204 cases identified in the screening program. Test whether the case-fatality rate
Provide a 95% CI for the incidence rate of neuroblastoma in the screened population. Express the 95% CI as (p1, p2), where p1 and p2 are in the units of number of cases per 100,000 children. Is p0
Test whether the number of cases detected by the screening program is significantly greater than expected?CancerA screening program for neuroblastoma (a type of cancer) was undertaken in Germany
For what proportion of samples do you declare a significant difference? What should this proportion be for a large number of simulated samples?SimulationConsider the birth-weight data in Example 7.2.
What is the principal advantage of the contralateral design?What is your best estimate of the number of breast-cancer cases that would be prevented from age 40 to 70 if all women in the U.S.
Now assume that the true mean birth-weight is 115oz and repeat the exercise in Problem 7.86, assuming that the other conditions stated in Problem 7.86 are still correct?SimulationConsider the
More left eyes seem to be assigned to A than to P, and the investigator wonders whether the assignments are really random. Perform a significance test to assess how well the randomization is
What test can be used to test the hypothesis that the mean degree of itching is the same for active vs. placebo eyes? Table 7.10 Itching scores reported by participants aItching score left
Implement the test in Problem 7.77 using a two-sided test (report a p-value)?Table 7.10 Itching scores reported by participants aItching score left eye itching score right eye. Eye
Perform a hypothesis test to assess whether there are significant differences in mean BMD for the femoral neck between the heavier- and lighter-smoking twins?Table 7.10 Itching scores reported by
What should this proportion be for a large number of simulated samples? How do the results in Problem 7.86 compare with this?SimulationConsider the birth-weight data in Example 7.2.
Answer Problem 7.79 for mean BMD at the femoral shaft?Table 7.10 Itching scores reported by participants aItching score left eye itching score right eye. Eye Difforence Subject L.
Give an estimate for the incidence of HIV per 100 person-years among women who reside in neighborhoods with above-median numbers of sexual partners among men, and an estimate for the 5-year
Provide a 95% CI for the estimate in Problem 7.81?Infectious DiseaseConcurrent sexual partnerships are widely believed to be one of the main drivers of the HIV epidemic in sub-Saharan Africa. F.
Suppose 100 women who reside in a neighborhood with above-median numbers of sexual partners among men are followed for an average of 5 years. What is the probability that exactly 20 of the women will
What is the probability that 20 or more of these women will develop HIV?Infectious DiseaseConcurrent sexual partnerships are widely believed to be one of the main drivers of the HIV epidemic in
Assume the rate of HIV in neighborhoods with below the median number of sexual partners is known (without error) to be 3.15 cases per 100 person years. Test whether the rate in women from
Suppose that the true mean birth-weight for the low- SES babies is 120 oz, the true standard deviation is 24 oz, and the distribution of birth-weights is normal. Generate 100 random samples of size
Suppose 100 million women in the U.S. population Haven not developed breast cancer by the age of 40?CancerBreast cancer is strongly influenced by a woman’s reproductive history. In particular, the
Provide a 95% CI for the true incidence rate of breast cancer over the period from age 40 to 70 in this special subgroup?CancerBreast cancer is strongly influenced by a woman’s reproductive
Test the hypothesis that the underlying rate of breast cancer is the same or different in this group as in the general population?CancerBreast cancer is strongly influenced by a woman’s
Interpret the results for Problems 7.69 and 7.70?CancerThe combination of photochemotherapy with oral methoxsalen (psoralen) and ultraviolet A radiation (called PUVA treatment) is an effective
Provide a 95% CI for the expected number of events in the group with ¥ 250 treatments? CancerThe combination of photochemotherapy with oral methoxsalen (psoralen) and ultraviolet A
Suppose we want to compare the observed and expected number of events among the group with <250 treatments. Perform an appropriate significance test, and report a two-tailed p-value?CancerThe
Use hypothesis-testing methods to assess whether either treatment affects blood pressure or heart rate in patients with severe angina?
Apply hypothesis-testing methods to answer the questions posed in Problem 4.53?
Answer Problem 7.65 for the percentage of calories from fat (separately for total fat and saturated fat) as reported on the diet record and the food-frequency questionnaire. Assume there are 9
Assess whether reported nutrient consumption (saturated fat, total fat, alcohol consumption, total caloric intake) is comparable for the diet record and the food-frequency questionnaire. Use either
How many participants would be needed to have a 90% chance of finding a significant difference in mean cholesterol lowering between the high- and low-fiber diets if the high-fiber diet lowers mean
What is the approximate standard error of the mean for the high-fiber compared with the low-fiber diet (that is, the mean difference in cholesterol level between high- and low-fiber diets)?Nutrition,
Test the hypothesis that the high-fiber diet has a differential effect on cholesterol levels compared with a low fiber diet (report your results as p < .05 or p > .05)?Nutrition, Cardiovascular
Test the hypothesis that the low-fiber diet has an effect on cholesterol levels as compared with baseline (report your results as p < .05 or p > .05)?Nutrition, Cardiovascular DiseasePrevious
Test the hypothesis that the high-fiber diet has an effect on cholesterol levels as compared with baseline (report your results as p < .05 or p > .05)?Nutrition, Cardiovascular DiseasePrevious
Since this was a pilot study, the main question of interest is how many subjects would be needed to detect an increase of 10 g in mean LVM over 4 years using a twosided test with α =
Provide a 95% CI for the change in LVM over 4 years based on the data in Table 7.6?Cardiovascular Disease, PediatricsLeft ventricular mass (LVM) is an important risk factor for subsequent
Implement the test in Problem 7.56 and provide a two-tailed p-value.Cardiovascular Disease, PediatricsLeft ventricular mass (LVM) is an important risk factor for subsequent cardiovascular disease. A
What test can be used to assess if there is a change in mean LVM over 4 years? Cardiovascular Disease, PediatricsLeft ventricular mass (LVM) is an important risk factor for subsequent
Construct a 95% CI for the 5-year true rate of cataracts among the excessive-sunlight-exposure group?The researchers decide to extend the study to a 5-year period and find that 20 of the 200 people
Test the hypothesis that the 5-year incidence rate of cataracts is different in the excessive-sunlight-exposure group compared with the general population, and report a p-value (two-sided). The
Implement the test procedure in Problem 7.52, and report a p-value (two-sided)?OphthalmologyResearchers have reported that the incidence rate of cataracts may be elevated among people with excessive
What test procedure can be used to compare the 1-year rate of cataracts in this population with that in the general population? OphthalmologyResearchers have reported that the incidence rate of
Perform a significance test to assess whether there is an association between mortality from cirrhosis of the liver and duration of employment in the group hired after 1945. Report a
A similar analysis was performed among workers who were hired after 1945 and who were employed for 10 or more years. It found 4 deaths from cirrhosis of the liver, whereas only 3.4 were expected.
Perform a significance test to assess whether there is an association between long duration of employment and mortality from cirrhosis of the liver in the group hired prior to 1946. Report a
What is the SMR for this group? Occupational HealthThe mortality experience of 8146 male employees of a research, engineering, and metal-fabrication plant in Tonawanda, New York, was studied
Suppose that four cases are observed over 1 year among 300 girls 0–4 years of age with smoking mothers. Answer Problem 7.17 based on these data?Pulmonary DiseaseSuppose the annual incidence of
Report a p-value corresponding to your answer to Problem 7.17?Pulmonary DiseaseSuppose the annual incidence of asthma in the general population among children 0–4 years of age is 1.4% for boys and
If 10 cases are observed over 1 year among 500 boys 0–4 years of age with smoking mothers, then test whether there is a significant difference in asthma incidence between this group and the general
How large a sample is needed in Problem 7.15 to achieve 90% power?Suppose that 25% of patients with MI in 2000 died within 24 hours. This proportion is called the 24-hour case-fatality rate.
Suppose we eventually plan to accumulate 50 MI cases during the period 2010–2015. Assume that the 24-hour case-fatality rate is truly 20% during this period. How much power would such a study have
Report a p-value to correspond to your answer to Problem 7.12?Cardiovascular DiseaseSuppose the incidence rate of myocardial infarction (MI) was 5 per 1000 among 45- to 54-year-old men in 2000. To
Using the critical-value method with α = .05, test the hypothesis that incidence rates of MI changed from 2000 to 2010?Cardiovascular DiseaseSuppose the incidence rate of myocardial infarction (MI)
How many people would need to be studied to have 80% power under the assumptions in Problem 7.9?DiabetesPlasma-glucose levels are used to determine the presence of diabetes. Suppose the mean ln
Answer Problem 7.9 if the expected difference is 0.20 ln units?DiabetesPlasma-glucose levels are used to determine the presence of diabetes. Suppose the mean ln (plasma-glucose) concentration (mg/dL)
If the expected difference is 0.10 ln units, then what is the power of such a study if a two-sided test is to be used with α = .05? DiabetesPlasma-glucose levels are used to determine the
The FDA will approve the new test if the lower bound of a 90% CI for the mean score is ≥+5. Should the FDA approve the test? A yes/no answer is not sufficient. Suppose a quality score is
Provide a 95% CI for the specificity?GeneralSuppose a new test is proposed to identify patients with a specific condition.One specimen is obtained from each of 220 subjects in the population to whom
What is the estimated specificity of the test?GeneralSuppose a new test is proposed to identify patients with a specific condition.One specimen is obtained from each of 220 subjects in the population
Provide a 95% CI for the sensitivity?GeneralSuppose a new test is proposed to identify patients with a specific condition.One specimen is obtained from each of 220 subjects in the population to whom
What is the estimated sensitivity of the test? GeneralSuppose a new test is proposed to identify patients with a specific condition.One specimen is obtained from each of 220 subjects in the
Compare the inferences you made from the procedures in Problems 7.39, 7.40, and 7.41?The standard deviation of daily iron intake in the larger population of 9- to 11-year-old boys was 5.56 mg. We
Compute a 95% CI for the underlying variance of daily iron intake in the low-income group. What can you infer from this CI?The standard deviation of daily iron intake in the larger population of 9-
What is the p-value for the test conducted in Problem 7.39? The standard deviation of daily iron intake in the larger population of 9- to 11-year-old boys was 5.56 mg. We want to test whether
Carry out the test in Problem 7.38 using the critical value method with an α level of .05, and summarize your findings?The standard deviation of daily iron intake in the larger population of 9- to
State the hypotheses that we can use to answer this question?The standard deviation of daily iron intake in the larger population of 9- to 11-year-old boys was 5.56 mg. We want to test whether the
What is the p-value for the test conducted in Problem 7.36? NutritionIron-deficiency anemia is an important nutritional health problem in the United States. A dietary assessment was performed on
Carry out the hypothesis test in Problem 7.35 using the critical-value method with an α level of .05, and summarize your findings?NutritionIron-deficiency anemia is an important nutritional health
State the hypotheses that we can use to consider this question?NutritionIron-deficiency anemia is an important nutritional health problem in the United States. A dietary assessment was performed on
If the proportion of deaths from ischemic heart disease (IHD) is 40% for all 15- to 64-year-old men in England and Wales, whereas 18 of the preceding 90 deaths are attributed to IHD, then answer
Answer Problem 7.32 using the data from four plants, and report a p-value?After reviewing the results from one plant, the company decides to expand its study to include results from three additional
Perform the hypothesis test, and report a p-value?Occupational HealthThe proportion of deaths due to lung cancer in males ages 15–64 in England and Wales during the period 1970–1972 was 12%.
Is a one-sided or two-sided test appropriate here? Occupational HealthThe proportion of deaths due to lung cancer in males ages 15–64 in England and Wales during the period 1970–1972 was
State the hypotheses to use in answering this question?Occupational HealthThe proportion of deaths due to lung cancer in males ages 15–64 in England and Wales during the period 1970–1972 was 12%.
Suppose we conduct a study of the preceding hypothesis based on 20 participants. What is the probability we will be able to reject H0 using a one-sided test at the 5% level if the true mean and
If μd = true mean difference in DBP between baseline and 1 month, then how many patients would be needed to have a 90% chance of detecting a significant change in DBP over 1 month using a one-tailed
Test the hypothesis that the incidence rate of nausea for the erythromycin group is the same for a typical pregnant woman?ObstetricsThe drug erythromycin has been proposed to possibly lower the risk
Suppose we identify 50 women 50 to 54 years of age who have both a mother and a sister with a history of breast cancer. Five of these women themselves have developed breast cancer at some time in
Which of the following sample results yields the smallest p-value and why?(i) x̅ = 28, s = 6(ii) x̅ = 27, s = 4(iii) x̅ = 32, s = 2(iv) x̅ = 26, s = 9Suppose we wish to test H0: μ = 30 vs. H1:
What will be the result if we conclude that the mean is 45 when the actual mean is 50?(i) We have made a type I error.(ii) We have made a type II error.(iii) We have made the correct
What will be the result if we conclude that the mean is greater than 45 when the actual mean is 45?(i) We have made a type I error.(ii) We have made a type II error.(iii) We have made the correct
Report a p-value corresponding to your results in Problem 7.21?GeneticsRibosomal 5S RNA can be represented as a sequence of 120 nucleotides. Each nucleotide can be represented by one of four
If the probability of an A in the 20th position in ribosomal 5S RNA is .79, then test the hypothesis that the new sequence is the same as ribosomal 5S RNA using the critical-value
Report a p-value corresponding to your answer to Problem 7.19?Pulmonary DiseaseSuppose the annual incidence of asthma in the general population among children 0–4 years of age is 1.4% for boys and
Assuming the two alleles of an individual are independent random variables, provide a point estimate and a 95% CI for the a allele frequency p?As an experiment, 10,000 people are completely
Does genotyping a population provide more accurate estimates of p than obtained by only having the clinical phenotype? Why or why not?As an experiment, 10,000 people are completely genotyped, of whom
Which of the following sample results yields a 95% CI for μ with the smallest width and why?(i) x = 28, s = 5, n = 61(ii) x = 32, s = 4, n = 30(iii) x = 25, s = 3, n = 20(iv) x = 40, s = 6, n =
Suppose we observe 30 cases of colon cancer over 35,000 person-years among women ages 50–54. Provide a point estimate and 95% CI for the incidence rate of colon cancer in this age-gender group?As
If the mean and standard deviation of serum creatinine in the general population are 1.0 and 0.4 mg/dL, respectively, then, using a significance level of .05, test whether the mean serum-creatinine
What is the p-value for the test?Renal DiseaseThe mean serum-creatinine level measured in 12 patients 24 hours after they received a newly proposed antibiotic was 1.2 mg/dL.
Suppose the sample standard deviation of serum creatinine in Problem 7.1 is 0.6 mg/dL. Assume that the standard deviation of serum creatinine is not known, and perform the hypothesis test in Problem
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