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biostatistics
Biostatistics A Foundation For Analysis In The Health Sciences 10th Edition Wayne W. Daniel, Chad L. Cross - Solutions
Explain the meaning of unbiasedness.
Why is estimation an important type of inference?
What is statistical inference?
Measurements of gastric secretion of hydrochloric acid (milliequivalents per hour) in 16 normal subjects and 10 subjects with duodenal ulcer yielded the following results:Normal subjects: 6.3, 2.0, 2.3, 0.5, 1.9, 3.2, 4.1, 4.0, 6.2, 6.1, 3.5, 1.3, 1.7, 4.5, 6.3, 6.2 Ulcer subjects: 13.7, 20.6,
Glucose responses to oral glucose were recorded for 11 patients with Huntington’s disease (group 1)and 13 control subjects (group 2). Statistical analysis of the results yielded the following sample variances: s2 1 ¼ 105;s2 2 ¼ 148.Construct the 95 percent confidence interval for the ratio of
Sample variances were computed for the tidal volumes (milliliters) of two groups of patients suffering from atrial septal defect. The results and sample sizes were as follows:n1 ¼ 31; s2 1 ¼ 35; 000 n2 ¼ 41; s2 2 ¼ 20; 000 Construct the 95 percent confidence interval for the ratio of the two
Thirty-two adult asphasics seeking speech therapy were divided equally into two groups. Group 1 received treatment 1, and group 2 received treatment 2.Statistical analysis of the treatment effectiveness scores yielded the following variances: s2 1 ¼ 8;s2 2 ¼ 15.Construct the 90 percent confidence
Stroke index values were statistically analyzed for two samples of patients suffering from myocardial infarction. The sample variances were 12 and 10.There were 21 patients in each sample. Construct the 95 percent confidence interval for the ratio of the two population variances.
The objective of a study by Horesh et al. (A-27) was to explore the hypothesis that some forms of suicidal behavior among adolescents are related to anger and impulsivity. The sample consisted of 65 adolescents admitted to a university-affiliated adolescent psychiatric unit. The researchers used
The purpose of a study by Moneim et al. (A-26) was to examine thumb amputations from team roping at rodeos. The researchers reviewed 16 cases of thumb amputations. Of these, 11 were complete amputations while five were incomplete. The ischemia time is the length of time that insufficient oxygen is
Twenty air samples taken at the same site over a period of 6 months showed the following amounts of suspended particulate matter (micrograms per cubic meter of air):68 22 36 32 42 24 28 38 30 44 28 27 28 43 45 50 79 74 57 21 Consider these measurements to be a random sample from a population of
Hemoglobin determinations were made on 16 animals exposed to a harmful chemical. The following observations were recorded: 15.6, 14.8, 14.4, 16.6, 13.8, 14.0, 17.3, 17.4, 18.6, 16.2, 14.7, 15.7, 16.4, 13.9, 14.8, 17.5. Construct 95 percent confidence intervals for s2 and s.
A sample of 25 physically and mentally healthy males participated in a sleep experiment in which the percentage of each participant’s total sleeping time spent in a certain stage of sleep was recorded. The variance computed from the sample data was 2.25. Construct 95 percent confidence intervals
In a study of myocardial transit times, appearance transit times were obtained on a sample of 30 patients with coronary artery disease. The sample variance was found to be 1.03. Construct 99 percent confidence intervals for s2 and s.
Forced vital capacity determinations were made on 20 healthy adult males. The sample variance was 1,000,000. Construct 90 percent confidence intervals for s2 and s.
Borden et al. (A-24) performed experiments on cadaveric knees to test the effectiveness of several meniscal repair techniques. Specimens were loaded into a servohydraulic device and tension-loaded to failure. The biomechanical testing was performed by using a slow loading rate to simulate the
A study by Aizenberg et al. (A-23) examined the efficacy of sildenafil, a potent phosphodiesterase inhibitor, in the treatment of elderly men with erectile dysfunction induced by antidepressant treatment for major depressive disorder. The ages of the 10 enrollees in the study were 74; 81; 70; 70;
A health planning agency wishes to know, for a certain geographic region, what proportion of patients admitted to hospitals for the treatment of trauma die in the hospital. A 95 percent confidence interval is desired, the width of the interval must be .06, and the population proportion, from other
A hospital administrator wishes to know what proportion of discharged patients is unhappy with the care received during hospitalization. How large a sample should be drawn if we let d ¼ :05, the confidence coefficient is .95, and no other information is available? How large should the sample be if
A survey is planned to determine what proportion of the high-school students in a metropolitan school system have regularly smoked marijuana. If no estimate of p is available from previous studies, a pilot sample cannot be drawn, a confidence coefficient of .95 is desired, and d ¼ :04 is to be
An epidemiologist wishes to know what proportion of adults living in a large metropolitan area have subtype ayr hepatitis B virus. Determine the sample size that would be required to estimate the true proportion to within .03 with 95 percent confidence. In a similar metropolitan area the proportion
For multiple sclerosis patients we wish to estimate the mean age at which the disease was first diagnosed. We want a 95 percent confidence interval that is 10 years wide. If the population variance is 90, how large should our sample be?
A physician would like to know the mean fasting blood glucose value (milligrams per 100 ml) of patients seen in a diabetes clinic over the past 10 years. Determine the number of records the physician should examine in order to obtain a 90 percent confidence interval for m if the desired width of
The director of the rabies control section in a city health department wishes to draw a sample from the department’s records of dog bites reported during the past year in order to estimate the mean age of persons bitten. He wants a 95 percent confidence interval, he will be satisfied to let d ¼
A hospital administrator wishes to estimate the mean weight of babies born in her hospital. How large a sample of birth records should be taken if she wants a 99 percent confidence interval that is 1 pound wide? Assume that a reasonable estimate of s is 1 pound. What sample size is required if the
To study the difference in drug therapy adherence among subjects with depression who received usual care and those who received care in a collaborative care model was the goal of a study conducted by Finley et al. (A-21). The collaborative care model emphasized the role of clinical pharmacists in
Spertus et al. (A-20) performed a randomized single blind study for subjects with stable coronary artery disease. They randomized subjects into two treatment groups. The first group had current angina medications optimized, and the second group was tapered off existing medications and then started
The objective of a randomized controlled trial by Adab et al. (A-19) was to determine whether providing women with additional information on the pros and cons of screening for cervical cancer would increase the willingness to be screened. A treatment group of 138 women received a leaflet on
Horwitz et al. (A-18) studied 637 persons who were identified by court records from 1967 to 1971 as having experienced abuse or neglect. For a control group, they located 510 subjects who as children attended the same elementary school and lived within a five-block radius of those in the
In a simple random sample of 125 unemployed male high-school dropouts between the ages of 16 and 21, inclusive, 88 stated that they were regular consumers of alcoholic beverages. Construct a 95 percent confidence interval for the population proportion.
In a study by von zur Muhlen et al. (A-16), 136 subjects with syncope or near syncope were studied.Syncope is the temporary loss of consciousness due to a sudden decline in blood flow to the brain. Of these subjects, 75 also reported having cardiovascular disease. Construct a 99 percent confidence
Q waves on the electrocardiogram, according to Schinkel et al. (A-15), are often considered to be reflective of irreversibly scarred myocardium. These researchers assert, however, that there are some indications that residual viable tissue may be present in Q-wave-infarcted regions. Their study of
Luna et al. (A-14) studied patients who were mechanically ventilated in the intensive care unit of six hospitals in Buenos Aires, Argentina. The researchers found that of 472 mechanically ventilated patients, 63 had clinical evidence of ventilator-associated pneumonia (VAP). Construct a 95 percent
In a study of factors thought to be responsible for the adverse effects of smoking on human reproduction, cadmium level determinations (nanograms per gram) were made on placenta tissue of a sample of 14 mothers who were smokers and an independent random sample of 18 nonsmoking mothers. The results
The average length of stay of a sample of 20 patients discharged from a general hospital was 7 days with a standard deviation of 2 days. A sample of 24 patients discharged from a chronic disease hospital had an average length of stay of 36 days with a standard deviation of 10 days. Assume normally
Two groups of children were given visual acuity tests. Group 1 was composed of 11 children who receive their health care from private physicians. The mean score for this group was 26 with a standard deviation of 5.Group 2 was composed of 14 children who receive their health care from the health
Twenty-four experimental animals with vitamin D deficiency were divided equally into two groups.Group 1 received treatment consisting of a diet that provided vitamin D. The second group was not treated. At the end of the experimental period, serum calcium determinations were made with the following
Transverse diameter measurements on the hearts of adult males and females gave the following results:Group Sample Size x (cm) s (cm)Males 12 13.21 1.05 Females 9 11.00 1.01 Assume normally distributed populations with equal variances.
Krantz et al. (A-12) investigated dose-related effects of methadone in subjects with torsade de pointes, a polymorphic ventricular tachycardia. In the study of 17 subjects, nine were being treated with methadone for opiate dependency and eight for chronic pain. The mean daily dose of methadone in
The purpose of a study by Nozawa et al. (A-11) was to determine the effectiveness of segmental wire fixation in athletes with spondylolysis. Between 1993 and 2000, 20 athletes (6 women and 14 men)with lumbar spondylolysis were treated surgically with the technique. The following table gives the
The objectives of a study by van Vollenhoven et al. (A-10) were to examine the effectiveness of etanercept alone and etanercept in combination with methotrexate in the treatment of rheumatoid arthritis. The researchers conducted a retrospective study using data from the STURE database, which
Chan et al. (A-9) developed a questionnaire to assess knowledge of prostate cancer. There was a total of 36 questions to which respondents could answer “agree,” “disagree,” or “don’t know.” Scores could range from 0 to 36.The mean scores for Caucasian study participants was 20.6 with
Iannelo et al. (A-8) performed a study that examined free fatty acid concentrations in 18 lean subjects and 11 obese subjects. The lean subjects had a mean level of 299 mEq/L with a standard error of the mean of 30, while the obese subjects had a mean of 744 mEq/L with a standard error of the mean
The subjects of a study by Dugoff et al. (A-5) were 10 obstetrics and gynecology interns at the University of Colorado Health Sciences Center. The researchers wanted to assess competence in performing clinical breast examinations. One of the baseline measurements was the number of such examinations
A sample of 16 ten-year-old girls had a mean weight of 71.5 and a standard deviation of 12 pounds, respectively. Assuming normality, find the 90, 95, and 99 percent confidence intervals for m.
The concern of a study by Beynnon et al. (A-4) were nine subjects with chronic anterior cruciate ligament (ACL) tears. One of the variables of interest was the laxity of the anteroposterior, where higher values indicate more knee instability. The researchers found that among subjects with
Pedroletti et al. (A-3) reported the maximal nitric oxide diffusion rate in a sample of 15 asthmatic schoolchildren and 15 controls as mean standard error of the mean. For asthmatic children, they reported 3:5 0:4 nL=s (nanoliters per second) and for control subjects they reported 0:7 :1 nL=s.For
In a study of the effects of early Alzheimer’s disease on nondeclarative memory, Reber et al. (A-2)used the Category Fluency Test to establish baseline persistence and semantic memory and language abilities. The eight subjects in the sample had Category Fluency Test scores of 11, 10, 6, 3, 11,
Use the t distribution to find the reliability factor for a confidence interval based on the following confidence coefficients and sample sizes:abcd Confidence coefficient .95 .99 .90 .95 Sample size 15 24 8 30
understand the basic properties and uses of the t distribution, chi-square distribution, and F distribution
be able to interpret a confidence interval from both a practical and a probabilistic viewpoint.
be able to calculate interval estimates for a variety of parameters.
understand the importance and basic principles of estimation.
For each of the following populations of measurements, state whether the sampling distribution of the sample mean is normally distributed, approximately normally distributed, or not approximately normally distributed when computed from samples of size (A) 10, (B) 50, and (C) 200.(a) The logarithm
Refer to Exercise 25.What is the probability that a single simple random sample of size 35 drawn from this population will yield a mean between 22 and 29?
Refer to Exercise 25.What will be the mean and variance of the sampling distribution?
The standard deviation was 7 years. Consider the sampling distribution of sample means based on samples of size 35 drawn from this population. What will be the shape of the sampling distribution?
In a population of subjects who died from lung cancer following exposure to asbestos, it was found that the mean number of years elapsing between exposure and death was
Refer to Exercise 22.What is the probability that a single simple random sample of size 110 drawn from this population will yield a sample proportion smaller than .50?
Refer to Exercise 22.Compute the mean and variance of the sampling distribution.
It is estimated by the 1999–2000 NHANES [A-7] that among adults 18 years old or older 53 percent have never smoked. Assume the proportion of U.S. adults who have never smoked to be .53. Consider the sampling distribution of the sample proportion based on simple random samples of size 110 drawn
How many simple random samples (without replacement) of size 5 can be selected from a population of size 10?
Use the information in Review Exercises 18 and 19 to find the probability that the difference in the cancer percentages between men and women will be less than 5 percent when 220 women and 250 men aged 65 and older are selected at random.
The cancer rate for men ages 65 and older is 23 percent. Use this estimate as the percentage of all men ages 65 and older who have been told by a health care provider that they have cancer. Find the probability that among 250 men selected at random that fewer than 20 percent will have been told
Refer to Review Exercise
Refer to Review Exercise 17.The reported cancer rate for women subjects ages 65 and older is 17 percent. Using this estimate as the true percentage of all females ages 65 and over who have been told by a health care provider that they have cancer, find the probability that if 220 women are selected
The results of the 1999 National Health Interview Survey released in 2003 [A-7] showed that among U.S. adults ages 60 and older, 19 percent had been told by a doctor or other health care provider that they had some form of cancer. If we use this as the percentage for all adults 65 years old and
Using the information in Review Exercises 14 and 15, and assuming independent random samples of size 100 and 120 for women and men, respectively, find the probability that the difference in sample mean iron levels is greater than 5 mg.
Refer to Review Exercise 14.The mean iron level for men between the ages of 20 and 39 years is 17.9 mg with an estimated standard deviation of 10.9 mg. Using 17.9 and 10.9 as population parameters, find the probability that a random sample of 120 men will have a mean iron level higher than 19 mg.
In the results published by Wright et al. [A-2] based on data from the 1999–2000 NHANES study referred to in Exercises 5.4.1 and 5.4.2, investigators reported on their examination of iron levels. The mean iron level for women ages 20–39 years was 13.7 mg with an estimated standard deviation of
Using the information in Review Exercises 11 and 12, find the probability that the difference in mean BMI for 45 women and 50 men selected independently and at random from the respective populations will exceed 3.
In the study cited in Review Exercise 11, the researchers reported the mean BMI for men ages 60 and older with normal skeletal muscle index to be 24.7 with a standard deviation of 3.3. Using these values as the population mean and standard deviation, find the probability that 50 randomly selected
Janssen et al. [A-10] studied Americans ages 60 and over. They estimated the mean body mass index of women over age 60 with normal skeletal muscle to be 23.1 with a standard deviation of 3.7. Using these values as the population mean and standard deviation for women over age 60 with normal skeletal
What is the probability that a random sample of 16 subjects will have a mean response time of 12 seconds or more?
Suppose it is known that the response time of healthy subjects to a particular stimulus is a normally distributed random variable with a mean of 15 seconds and a variance of
Explain the procedure you would follow in constructing the sampling distribution of the difference between sample proportions based on large samples from finite populations.
Describe the sampling distribution of the difference between two sample means when large samples are drawn.
Describe the sampling distribution of the sample proportion when large samples are drawn.
Describe the sampling distribution of the difference between two sample means.
How does the sampling distribution of the sample mean, when sampling is without replacement, differ from the sampling distribution obtained when sampling is with replacement?
Describe the sampling distribution of the sample mean when sampling is with replacement from a normally distributed population.
Explain how a sampling distribution may be constructed from a finite population.
From the results of a survey conducted by the U.S. Bureau of Labor Statistics [A-9], it was estimated that 21 percent of workers employed in the Northeast participated in health care benefits programs that included vision care. The percentage in the South was 13 percent. Assume these percentages
In the report cited in Exercise 5.6.1[A-8], the Census Bureau stated that for Americans in the age group 18–24 years, 64.8 percent had private health insurance. In the age group 25–34 years, the percentage was 72.1. Assume that these percentages are the population parameters in those age groups
According to the 2000 U.S. Census Bureau [A-8], in 2000, 9.5 percent of children in the state of Ohio were not covered by private or government health insurance. In the neighboring state of Pennsylvania, 4.9 percent of children were not covered by health insurance. Assume that these proportions are
It is known that 35 percent of the members of a certain population suffer from one or more chronic diseases. What is the probability that in a sample of 200 subjects drawn at random from this population 80 or more will have at least one chronic disease?
Given a population in which p ¼ :6 and a random sample from this population of size 100, find:(a) Pð Þ ^p :65 (b) Pð Þ ^p :58(c) Pð Þ :56 ^p :63
Gallagher et al. [A-6] reported on a study to identify factors that influence women’s attendance at cardiac rehabilitation programs. They found that by 12 weeks post-discharge, only 64 percent of eligible women attended such programs. Using 64 percent as an estimate of the attendance percentage
In the 1999-2000 NHANES report, researchers estimated that 64 percent of U.S. adults ages 20–74 were overweight or obese (overweight: BMI 25–29, obese: BMI 30 or greater). Use this estimate as the population proportion for U.S. adults ages 20–74. If 125 subjects are selected at random from
In the study cited in Exercise 5.5.1, 13 percent of the patients in the study reported previous episodes of stroke or transient ischemic attack. Use 13 percent as the estimate of the prevalence of stroke or transient ischemic attack within the population. If 70 subjects are chosen at random from
Smith et al. [A-5] performed a retrospective analysis of data on 782 eligible patients admitted with myocardial infarction to a 46-bed cardiac service facility. Of these patients, 248 (32 percent) reported a past myocardial infarction. Use .32 as the population proportion. Suppose 50 subjects are
For a population of 17-year-old boys and 17-year-old girls, the means and standard deviations, respectively, of their subscapular skinfold thickness values are as follows: boys, 9.7 and 6.0; girls, 15.6 and 9.5. Simple random samples of 40 boys and 35 girls are selected from the populations. What
Given two normally distributed populations with equal means and variances of s2 1 ¼ 240 and s2 2 ¼ 350, what is the probability that samples of size n1 ¼ 40 and n2 ¼ 35 will yield a value ofx1 x2 as large as or larger than 12?
Given two normally distributed populations with equal means and variances of s2 1 ¼ 100 and s2 2 ¼ 80, what is the probability that samples of size n1 ¼ 25 and n2 ¼ 16 will yield a value of x1 x2 greater than or equal to 8?
In the study cited in Exercises 5.3.4 and 5.3.5, the calcium levels in men and women ages 60 years or older are summarized in the following table:Mean Standard Deviation Men 797 482 Women 660 414 Use these estimates as the mean m and standard deviation s for the U.S. populations for these age
The study cited in Exercises 5.3.1 and 5.3.2 gives the following data on serum cholesterol levels in U.S. females:Population Age Mean Standard Deviation A 20–29 183 37.2 B 30–39 189 34.7 Use these estimates as the mean m and standard deviation s for the respective U.S. populations.Suppose we
Use the data cited in Exercise 5.3.1.Imagine we take samples of size 5, 25, 50, 100, and 500 from the women in this age group.(a) Calculate the standard error for each of these sampling scenarios.(b) Discuss how sample size affects the standard error estimates calculated in part (a) and the
Use the data of Example 5.3.1 to construct the sampling distribution of x based on samples of size 3 selected without replacement. Find the mean and variance of the sampling distribution.
Suppose a population consists of the following values: 1, 3, 5, 7, 9.Construct the sampling distribution of x based on samples of size 2 selected without replacement. Find the mean and variance of the sampling distribution.
Given m ¼ 50; s ¼ 16, and n ¼ 64, find:(a) Pð Þ 45 x 55 (b) Pð Þ x > 53(c) Pð Þ x < 47 (d) Pð Þ 49 x 56
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