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biostatistics
Biostatistics A Foundation For Analysis In The Health Sciences 7th Edition Wayne W Daniel - Solutions
3. List and explain each step in the nine-step hypothesis testing procedure.
2. What is a hypothesis?
1. What is the purpose of hypothesis testing?
36. Bellomo et al. (A-36) conducted a study to quantitate insulin losses and glucose absorption during acute continuous hemofiltration with dialysis and to assess the clinical importance of these changes. Subjects were 16 ICU patients with acute renal failure at a university medical center. The
35. The purpose of a study by Kay et al. (A-35) was to determine the safety and efficacy of radiofrequency ablation as definitive therapy for primary atrial tachycardias. Subjects were 15 consecutive patients with primary atrial arrhythmias that were refractory to medical management. The authors
34. Duncan et al. (A-34) report on a study designed to assess the relation of exclusive breastfeeding, independent of recognized risk factors, to acute and recurrent otitis media in the first 12 months of life. The subjects were 1220 infants who used a health maintenance organization. What was the
33. el Fiky et al. (A-33) measured shunt fraction invasively using a pulmonary artery catheter in 22 patients undergoing elective coronary artery surgery. From the results, the investigators computed a mean of 19.6 and constructed a 90 percent confidence interval for the population mean with
32. In general, a high level of confidence is preferred over a low level of confidence. For a given set of other conditions, suppose we set our level of confidence at 100 percent.What would be the effect of such a choice on the width of the interval?
31. In general, narrow confidence intervals are preferred over wide ones. We can make an interval narrow by using a small confidence coefficient. For a given set of other conditions, what happens to the level of confidence when we use a small confidence coefficient? What would happen to the
30. The objectives of a study by Steinhardt et al. (A-32) were (1) to determine if level of physical activity and cardiovascular fitness were significantly related to absenteeism and medical care claims among law enforcement officers over a one-year period and (2) to determine if moderate levels of
29. Osberg et al. (A-31) conducted a study to identify factors that predict whether or not similarly impaired children treated at trauma centers are discharged to inpatient rehabilitation. Among other findings by the investigators were the following: In a sample of 115 subjects discharged from a
28. In a study of the role of dietary fats in the etiology of ischemic heart disease the subjects were 60 males between 40 and 60 years of age who had recently had a myocardial infarction and 50 apparently healthy males from the same age group and social class.One variable of interest in the study
27. The purpose of a study by Thurnau et al. (A-30) was to evaluate the accuracy of the fetal—pelvic index disproportion and delivery outcome in gravid women attempting vaginal birth after previous cesarean delivery. Among the data reported were the following on birth weight (grams):Delivery
26. Harrison et al. (A-29) conducted a study of dependent elderly people in a London borough. Along with other characteristics, they collected data on the extent of depression among borough residents. In a sample of 158 subjects who had a previous diagnosis of depression, 48 were rated during the
25. The objective of a study by Martin et al. (A-28) was to compare the function of neutrophils in the pulmonary artery blood and lung lavage fluid of patients early in the course of adult respiratory distress syndrome. Of concern were three antibacterial functions: the release of reactive oxygen
24. Milliez et al. (A-27) conducted a study involving high-risk pregnancies. A sample of 23 nulliparous women delivered babies whose mean weight was 2958 grams with a standard deviation of 620. The mean and standard deviation of the weights of babies born to a sample of 26 multiparous women were
23. Drug A was prescribed for a random sample of 12 patients complaining of insomnia. An independent random sample of 16 patients with the same complaint received drug B.The numbers of hours of sleep experienced during the second night after treatment began were as follows:A: 3.5, 5.7, 3.4, 6.9,
22. Determinations of saliva pH levels were made in two independent random samples of seventh grade schoolchildren. Sample A children were caries-free while sample B children had a high incidence of caries. The results were as follows:A: 7.14, 7.11, 7.61, 7.98, 7.21, 7.16, 7.89 7.24, 7.86, 7.47,
21. What is the average serum bilirubin level of patients admitted to a hospital for treatment of hepatitis? A sample of 10 patients yielded the following results:20.5, 14.8, 21.3, 12.7, 15.2, 26.6, 23.4, 22.9, 15.7, 19.2 Construct a 95 percent confidence interval for the population mean.
20. Seventy patients with stasis ulcers of the leg were randomly divided into two equal groups. Each group received a different treatment for edema. At the end of the experiment, treatment effectiveness was measured in terms of reduction in leg volume as determined by water displacement. The means
19. A certain drug was found to be effective in the treatment of pulmonary disease in 180 of 200 cases treated. Construct the 90 percent confidence interval for the population proportion.
18. A breast cancer research team collected the following data on tumor size:Type of Tumor A 21 3.85 cm 1.95 cm B 16 2.80 cm 1.70 cm Construct a 95 percent confidence interval for the difference between population means.
17. In a dental survey conducted by a county dental health team, 500 adults were asked to give the reason for their last visit to a dentist. Of the 220 who had less than a high school education, 44 said they went for preventive reasons. Of the remaining 280, who had a high school education or
16. Refer to the previous problem. How large a sample would be required to estimate the population proportion to within .05 with 95 percent confidence (.3Q is the best available estimate of p):a. If the finite population correction can be ignored?b. If the finite population correction is not
15. An industrial hygiene survey was conducted in a large metropolitan area. Of 70 manufacturing plants of a certain type visited, 21 received a "poor" rating with respect to absence of safety hazards. Construct a 95 percent confidence interval for the population proportion deserving a "poor"
14. What proportion of asthma patients are allergic to house dust? In a sample of 140, 35 percent had positive skin reactions. Construct the 95 percent confidence interval for the population proportion.
13. Arterial blood gas analyses performed on a sample of 15 physically active adult males yielded the following resting Pa02 values:75, 80, 80, 74, 84, 78, 89, 72, 83, 76, 75, 87, 78, 79, 88 Compute the 95 percent confidence interval for the mean of the population.
12. What are the assumptions underlying the use of the t distribution in estimating the difference between two population means?
11. What is the finite population correction? When can it be ignored?
10. What are the assumptions underlying the use of the t distribution in estimating a single population mean?
9. Describe the t distribution.
8. Of what use is the central limit theorem in estimation?
7. State the probabilistic and practical interpretations of a confidence interval.
6. Give the general formula for a confidence interval.
5. Define the following:a. Reliability coefficientb. Confidence coefficientc. Precisiond. Standard errore. Estimatorf. Margin of error
4. Explain the meaning of unbiasedness.
3. What is a point estimate?
2. Why is estimation an important type of inference?
1. What is statistical inference?
34. Explain why each of the following measurements is or is not the result of a Bernoulli trial:a. The number of surgical procedures performed in a hospital in a week.b. A Hospital patient's temperature in degrees Celsius.c. A hospital patient's vital signs recorded as normal or not normal.
33. Explain why each of the following measurements is or is not the result of a Bernoulli trial:a. The gender of a newborn child.b. The classification of a hospital patient's condition as stable, critical, fair, good, or poor.c. The weight in grams of a newborn child.
32. Given the normally distributed random variable X with p, = 30 and P(X < 50) = .9772, find cr.
31. Given the normally distributed random variable X with p. = 25 and P(X 5 10) = .0778, find cr.
30. Given the normally distributed random variable X with et = 5 and P(X 25) = .0526, find p..
29. Given the normally distributed random variable X witha- = 15 and P(X < 50) = .9904, find p.
28. Given the normally distributed random variable X with o = 10 and P(X < 40) = .0080, find tk.
27. Given the normally distributed random variable X with mean 100 and standard deviation 15, find the numerical value of k such that:a. P(X < k) = .0094b. P(X k) = .1093c. P(100 < X < k) = .4778d. P(k' < X < k) = .9660, where k' and k are equidistant from
26. Given the normally distributed random variable X, find the numerical value of k such that P(p, — ko- + Ica) = .754.
25. Suppose a variable X is normally distributed with a standard deviation of 10. Given that.0985 of the values of X are greater than 70, what is the mean value of X?
24. Given a binomial variable with a mean of 20 and a variance of 16, find n and p.
23. Scores made on a certain aptitude test by nursing students are approximately normally distributed with a mean of 500 and a variance of 10,000.a. What proportion of those taking the test score below 200?b. A person is about to take the test; what is the probability that he or she will make a
22. A nurse supervisor has found that staff nurses, on the average, complete a certain task in 10 minutes. If the times required to complete the task are approximately normally distributed with a standard deviation of 3 minutes, find:a. The proportion of nurses completing the task in less than 4
21. The IQs of individuals admitted to a state school for the mentally retarded are approximately normally distributed with a mean of 60 and a standard deviation of 10.a. Find the proportion of individuals with IQs greater than 75.b. What is the probability that an individual picked at random will
20. In a certain metropolitan area there is an average of one suicide per month. What is the probability that during a given month the number of suicides will be:a. Greater than one?b. Less than one?c. Greater than three?
19. On the average, five smokers pass a certain street corner every 10 minutes. What is the probability that during a given 10-minute period the number of smokers passing will be:a. Six or fewer?b. Seven or more?c. Exactly eight?
18. On the average, two students per hour report for treatment to the first-aid room of a large elementary school.a. What is the probability that during a given hour three students come to the first-aid room for treatment?b. What is the probability that during a given hour two or fewer students
17. In a certain developing country, 30 percent of the children are undernourished. In a random sample of 25 children from this area, what is the probability that the number of undernourished will be:a. Exactly 10?b. Less than five?c. Five or more?d. Between three and five inclusive?e. Less than
16. Personnel records of a large hospital show that 10 percent of housekeeping and maintenance employees quit within one year after being hired. If 10 new employees have just been hired:a. What is the probability that exactly half of them will still be working after one year?b. What is the
15. The usual method for teaching a particular self-care skill to retarded persons is effective in 50 percent of the cases. A new method is tried with 10 persons. If the new method is no better than the standard, what is the probability that seven or more will learn the skill?
14. Using the data of your answer to question 13, demonstrate the use of the standard normal distribution in answering probability questions related to the variable selected.
13. Give an example of a random variable that you think is, at least approximately, normally distributed.
12. Describe the standard normal distribution and tell how it is used in statistics.
11. Describe the normal distribution.
10. Give an example of a random variable that you think is distributed according to the Poisson law.
9. Describe the Poisson distribution.
8. Give an example of a random variable that you think follows a binomial distribution.
7. Describe the binomial distribution.
6. What is a Bernoulli trial?
5. What is a cumulative probability distribution?
4. Define the probability distribution of a continuous random variable.
3. Define the probability distribution of a discrete random variable.
2. What is a continuous random variable? Give three examples of interest to the health professional.
1. What is a discrete random variable? Give three examples that are of interest to the health professional.
4.6.14 Given the following probability, find z1:P(. 5. < 2.98) = .1117
4.6.12 Given the following probability, find z1:P(— 2.67 zi) = .9718
4.6.15 Given the following probability, find z1:P( — z1 _5 z zi) = .8132
4.6.13 Given the following probability, find z1:/3(z. > z,) = .0384
4.6.11 Given the following probability, find z1:P(z < zi) = .0055
4.6.9 P( — 1.65 < z < 1.65). 4.6.10 P(z = .74).
4.6.7 P( — 1.96 < z < 1.96). 4.6.8 — 2.58 < z < 2.58).
4.6.5 P(z < —2.33). 4.6.6 P(z < 2.33).
4.6.3 P(z .55). 4.6.4 P(z > — .55).
4.6.2 The probability that a z picked at random will have a value between z = —2.87 and Z = 2.64.
4.6.1 The area under the curve between z = 0 and z = 1.43.
4.4.5 In a certain population an average of 13 new cases of esophageal cancer are diagnosed each year. If the annual incidence of esophageal cancer follows a Poisson distribution, find the probability that in a given year the number of newly diagnosed cases of esophageal cancer will be:a. Exactly
4.4.4 In a study of the effectiveness of an insecticide against a certain insect, a large area of land was sprayed. Later the area was examined for live insects by randomly selecting squares and counting the number of live insects per square. Past experience has shown the average number of live
4.4.3 If the mean number of serious accidents per year in a large factory (where the number of employees remains constant) is five, find the probability that in the current year there will be:a. Exactly seven accidents.b. Ten or more accidents.c. No accidents.d. Fewer than five accidents.
4.4.2 Suppose that over a period of several years the average number of deaths from a certain noncontagious disease has been 10. If the number of deaths from this disease follows the Poisson distribution, what is the probability that during the current year:a. Exactly seven people will die from the
4.4.1 Suppose it is known that in a certain area of a large city the average number of rats per quarter block is five. Assuming that the number of rats follows a Poisson distribution, find the probability that in a randomly selected quarter block:a. There are exactly five rats.b. There are more
20. Refer to Exercise 18. State in words the meaning of the following events:a. iTb. Bc. C
19. Refer to Exercise 18. State in words the meaning of the following events:a. A U Bb. A n Bc. A n cd. A U C
18. For a certain population we define the following events with respect to plasma lipoprotein levels (mg/dl): A = (10-15); B = 30); C = 20). Are the events A and B mutually exclusive? A and C? B and C? Explain your answer to each question.
17. Refer to Exercise 14. Comment on the event G = (A n B).
16. Refer to Exercise 14. State in words the event F = C).
15. Refer to Exercise 14. State in words the event E = (A U B).
14. For a certain population we define the following events for mother's age at time of giving birth: A = under 20 years; B = 20-24 years; C = 25-29 years; D = 30-44 years.Are the events A, B, C, and D pairwise mutually exclusive?
13. The probability that a person selected at random from a population will exhibit the classic symptom of a certain disease is .2, and the probability that a person selected at random has the disease is .23. The probability that a person who has the symptom also has the disease is .18. A person
12. In a certain population of women 4 percent have had breast cancer, 20 percent are smokers, and 3 percent are smokers and have had breast cancer. A woman is selected at random from the population. What is the probability that she has had breast cancer or smokes or both?
11. Suppose that 3 percent of the people in a population of adults have attempted suicide. It is also known that 20 percent of the population are living below the poverty level. If these two events are independent, what is the probability that a person selected at random from the population will
10. In a certain population the probability that a randomly selected subject will have been exposed to a certain allergen and experience a reaction to the allergen is .60. The probability is .8 that a subject exposed to the allergen will experience an allergic reaction. If a subject is selected at
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