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biostatistics

Biostatistics For The Biological And Health Sciences 2nd Edition Marc Triola, Mario Triola, Jason Roy - Solutions

3. Coughlin et al. (A-9) examined the breast and cervical screening practices of Hispanic and non-Hispanic women in counties that approximate the US. southern border region. The study used data from the Behavioral Risk Factor Surveillance System surveys of adults age 18 years or older conducted in
2. Name and explain the three properties of probability. (b) Objective probability (d) Classical probability (f) Mutually exclusive events (h) Marginal probability (j) Conditional probability (1) The multiplication rule (n) False positive (p) Sensitivity (r) Predictive value positive (t) Bayes's
1. Define the following: (a) Probability (c) Subjective probability (e) The relative frequency concept of probability (g) Independence (i) Joint probability (k) The addition rule (m) Complementary events (o) False negative (g) Specificity (s) Predictive value negative
3.5.3 Oexle et al. (A-7) calculated the negative predictive value of a test for carriers of X-linked ornithine transcarbamylase deficiency (OTCD-a disorder of the urea cycle). A test known as the "allopurinol test" is often used as a screening device of potential carriers whose rel- atives are OTCD
3.5.2 In an article entitled "Bucket-handle Meniscal Tears of the Knee: Sensitivity and Specificity of MRI signs, Dorsay and Helms (A-6) performed a retrospective study of 71 knees scanned by MRI. One of the indicators they examined was the absence of the "bow tiesign" in the MRI as evidence of a
3.5.1 A medical research team wishes to assess the usefulness of a certain symptom (call it $) in the diagnosis of a particular disease. In a random sample of 775 patients with the disease, 744 reported having the symptom. In an independent random sample of 1380 subjects without the disease, 21
29. Thilothammal et al. (A-19) designed a study to determine the efficacy of BCG (bacillus Calmette Gurin) vaccine in preventing tuberculous meningitis. Among the data collected on each subject was a measure of nutritional status (actual weight expressed as a percent- age of expected weight for
27. Refer to Exercise 2.3.12. Compute the mean, median, variance, standard deviation, first quartile, third quartile, and interquartile range. Construct a boxplot of the data. Are the mode, median, and mean equal? If not, explain why. Discuss the data in terms of variability. Compare the IQR with
26. Indicate for the following variables which you think would be a better measure of central tendency, the mean, the median, or mode, and justify your choice: 27. 28. (a) Annual incomes of licensed practical nurses in the Southeast. (b) Diagnoses of patients seen in the emergency department of a
25. Give a health sciences-related example of a population of measurements for which the median would be a better measure of central tendency than the mean.
24. Give a health sciences-related example of a population of measurements for which the mean would be a better measure of central tendency than the median.
23. On a statistics test students were asked to construct a frequency distribution of the blood Creatine levels (units/liter) for a sample of 300 healthy subjects. The mean was 95, and the standard deviation was 40. The following class interval widths were used by the students: (d) 15 (a) 1 (b) 5
22. Consider the following possible class intervals for use in constructing a frequency distri- bution of serum cholesterol levels of subjects who participated in a mass screening: (a) 50-74 (b) 50-74 (e) 50-75 75-99 75-99 75-100 100-149 100-124 100-125 150-174 125-149 125-150 175-199 150-174
21. Your statistics instructor tells you on the first day of class that there will be five tests dur ing the term. From the scores on these tests for each student, the instructor will compute a measure of central tendency that will serve as the student's final course grade. Before taking the first
20. Express in words the following properties of the sample mean: (a) (x) a minimum (b) nx-x (c) (x-x)=0
19. Spivack (A-18) investigated the severity of disease associated with C. difficille in pediatric inpatients. One of the variables they examined was number of days patients experienced diarrhea. The data for the 22 subjects in the study appear below. Compute the mean, median, variance, and
18. The following table shows the age distribution of live births in Albany County, New York State for 2000. Mother's Age Number of Live Births 10-14 7 15-19 258 20-24 585 25-29 841 30-34 981 35-39 526 40-44 99 45-19* 4 SOURCE: New York State Department of Health, Annual Vital Statistics 2000,
17. Give three synonyms for variation (variability).
16. The following are the cystatin C levels (mg/L) for the patients described in Exercise 15 (A-17). Cystatin C is a 'cationic basic protein that was investigated for its relationship to CFR levels. In addition, creatinine levels are also given. (Note: Some subjects were mea- sured more than once.)
15. Krieser et al. (A-17) examined glomerular filtration rate (GFR) in pediatric renal transplant recipients. GFR is an important parameter of renal function assessed in renal transplant recipients. The following are measurements from 19 subjects of GFR measured with dieth- ylenetriamine
14. The following table gives the age distribution for the number of deaths in New York State due to accidents for residents age 25 and older. 15. Age (years) Number of Deaths Due to Accidents 25-34 393 35-44 514 45-54 460 55-64 341 65-24 365 75-84 616 85-94* 618 SOURCE: New York State Department
13. Johnson et al. (A-16) performed a retrospective review of 50 fetuses that underwent open fetal myelomeningocele closure. The data below show the gestational age in weeks of the 50 fetuses undergoing the procedure.25 25 26 27 29 29 29 30 30 31 32 32 52 33 33 33 83 34 34 84 85 35 35 3.5 35 35 35
12. The purpose of a study by Tam et al. (A-15) was to investigate the wheelchair maneuvering in individuals with lower-level spinal cord injury (SCI) and healthy controls. Subjects used a modified wheelchair to incorporate a rigid seat surface to facilitate the specified exper imental
11. Find an article in a journal from your field of study in which some measure of central ten- dency and dispersion have been computed.
10. Compute the mean, median, mode, variance, and standard deviation for the data in Exer- cise 9.
9. Collect a set of real, or realistic, data from your field of study and construct a frequency distribution, a relative frequency distribution, a histogram, and a frequency polygon.
8. Describe from your field of study a population of data where knowledge of the central ten- dency and dispersion would be useful. Obtain real or realistic synthetic values from this population and compute the mean, median, mode, variance, and standard deviation.
7. What is another name for the 50th percentile (second or middle quartile)?
6. What is the purpose of Sturges's rule?
5. What is the purpose of the coefficient of variation?
4. Explain the rationale for using n-1 to compute the sample variance.
3. What are the advantages and limitations of the range as a measure of dispersion?
2. Define and compare the characteristics of the mean, the median, and the mode.
1. Define: (a) Stem-and-leaf display (c) Percentile (e) Location parameter (g) Ordered array (b) Box-and-whisker plot (d) Quartile (f) Exploratory data analysis (b) Frequency distribution (i) Relative frequency distribution (j) Statistic (k) Parameter (m) True class limits (1) Frequency polygon (n)
The purpose of a study by Nozawa et al. (A-13) was to evaluate the outcome of surgical repair of pars interarticularis defect by segmental wire fixation in young adults with lum- bar spondylolysis. The authors found that segmental wire fixation historically has been suc cessful in the treatment of
2.5.5 Cardosi et al. (A-12) performed a 4-year retrospective review of 102 women undergoing radical hysterectomy for cervical or endometrial cancer. Catheter-associated urinary tract infection was observed in 12 of the subjects. Below are the numbers of postoperative days until diagnosis of the
2.5.4 According to Starch et al. (A-11), hamstring tendon grafts have been the "weak link* in anterior cruciate ligament reconstruction. In a controlled laboratory study, they compared two techniques for reconstruction: either an interference screw or a central sleeve and screw on the tibial side.
Butz et al. (A-10) evaluated the duration of benefit derived from the use of noninvasive positive-pressure ventilation by patients with amyotrophic lateral sclerosis on symptoms, quality of life, and survival. One of the variables of interest is partial pressure of arterial carbon dioxide (PaCO2).
Shair and Anna Jasper, "Decreased Venous Return Is neither Sufficient nor Necessary to Elicit Ultrasonic Vocalization of Infant Rat Pups," Behavioral Neurosdence, 117 (2003), 840-853.
Porcellini et al. (A-8) studied 13 HIV-positive patients who were treated with highly active antiretroviral therapy (HAART) for at least 6 months. The CD4 T cell counts (x 10"/1) at baseline for the 13 subjects are listed below. 230 205 313 207 227 245 173 58 103 181 105 301 169 SOURCE: Simona
Number Needed to Treat Find the number of Viagra users that would need to stop using Viagra in order to prevent a single headache.
Absolute Risk Reduction Find the value of the absolute risk reduction for headaches in the treatment and placebo groups.
Comparing Probabilities Compare P(headache Viagra treatment) and P(headache placebo).
Probability For those in the Viagra treatment group, find the probability that the subject experienced a headache.
Type of Study Is the study retrospective or prospective?
Retrospective , Prospective The odds ratio is a measure used in retrospective or prospective studies. Describe retrospective and prospective studies.
Number Needed to Treat A measure of the effectiveness of an influenza vaccine is the number needed to treat, which is 37 (under certain conditions). Interpret that number. Does the result apply to every particular group of 37 subjects?
Relative Risk Identify an important disadvantage of relative risk used with a relatively small difference between the rates in the treatment and control groups.
Notation The relative risk of a characteristic is the ratio pt>pc. What do pt and pc represent?
Composite Water Samples The Fairfield County Department of Public Health tests water for the presence of E. coli (Escherichia coli) bacteria. To reduce laboratory costs, water samples from 10 public swimming areas are combined for one test, and further testing is done only if the combined sample
Composite Drug Test Based on the data in Table 4-1 on page 146, assume that the probability of a randomly selected person testing positive for drug use is 0.126. If drug screening samples are collected from 5 random subjects and combined, find the probability that the combined sample will reveal a
Redundancy in Hospital Generators Assume that emergency backup generators fail 22% of the times when they are needed (based on data from Arshad Mansoor, senior vice president with the Electric Power Research Institute). A hospital has three backup generators so that power is available if at least
Redundancy in Computer Hard Drives Assume that there is a 3% rate of disk drive failures in a year (based on data from various sources including lifehacker.com).a. If all of your computer data are stored on a hard disk drive with a copy stored on a second hard disk drive, what is the probability
Negative Predictive Value Find the negative predictive value for the test. That is, find the probability that a subject does not have hepatitis C, given that the test yields a negative result.Does the result make the test appear to be effective?
Positive Predictive Value Find the positive predictive value for the test. That is, find the probability that a subject has hepatitis C, given that the test yields a positive result. Does the result make the test appear to be effective?
False Negative Find the probability of selecting a subject with a negative test result, given that the subject has hepatitis C. What would be an unfavorable consequence of this error?
False Positive Find the probability of selecting a subject with a positive test result, given that the subject does not have hepatitis C. Why is this case problematic for test subjects?
Fraternal Twins If a pregnant woman is told that she will give birth to fraternal twins, what is the probability that she will give birth to two girls?
Fraternal Twins If a pregnant woman is told that she will give birth to fraternal twins, what is the probability that she will have one child of each gender?
Fraternal Twinsa. After having a sonogram, a pregnant woman learns that she will have twins. What is the probability that she will have fraternal twins?b. After studying the sonogram more closely, the physician tells the pregnant woman that she will give birth to twins consisting of one boy and one
Identical Twinsa. After having a sonogram, a pregnant woman learns that she will have twins. What is the probability that she will have identical twins?b. After studying the sonogram more closely, the physician tells the pregnant woman that she will give birth to twin boys. What is the probability
Fruit Flies An experiment with fruit flies involves one parent with normal wings and one parent with vestigial wings. When these parents have an offspring, there is a 3>4 probability that the offspring has normal wings and a 1>4 probability of vestigial wings. If the parents give birth to five
At Least One Defective Ultrasound Transducer A study showed that 39.8% of ultrasound transducers are defective (based on data from “High Incidence of Defective Ultrasound Transducers in Use in Routine Clinical Practice,” by Martensson et al., European Journal of Echocardiography, Vol. 10, No.
At Least One Correct Answer If you make random guesses for 10 multiple-choice MCAT test questions (each with five possible answers), what is the probability of getting at least 1 correct? If these questions are part of a practice test and an instructor says that you must get at least one correct
Phone Survey Subjects for the California Health Interview Survey are contacted using telephone numbers in which the last four digits are randomly selected (with replacement). Find the probability that for one such phone number, the last four digits include at least one 0.
Births in China In China, where many couples were allowed to have only one child, the probability of a baby being a boy was 0.545. Among six randomly selected births in China, what is the probability that at least one of them is a girl? Could this system continue to work indefinitely? (Phasing out
Births in the United States In the United States, the true probability of a baby being a boy is 0.512 (based on the data available at this writing). Among the next six randomly selected births in the United States, what is the probability that at least one of them is a girl?
Probability of a Girl Assuming that boys and girls are equally likely, find the probability of a couple having a boy when their third child is born, given that the first two children were both girls.
Three Girls Find the probability that when a couple has three children, at least one of them is a girl. (Assume that boys and girls are equally likely.)
Confusion of the Inverse Using the same events G and Y described in Exercise 3, describe confusion of the inverse.
Notation Let event G = subject has glaucoma (disorder of the eye) and let event Y = test indicates that “yes,” the subject has glaucoma. Use your own words to translate the notation P1Y G2 into a verbal statement.
Probability of At Least One Let A = the event of getting at least 1 defective pacemaker battery when 3 batteries are randomly selected with replacement from a batch. If 5% of the batteries in a batch are defective and the other 95% are all good, which of the following are correct?a. P1A2 =
Language: Complement of “At Least One” Let A = the event of getting at least one defective pacemaker battery when 3 batteries are randomly selected with replacement from a batch. Write a statement describing event A.
Medical Helicopters In a study of helicopter usage and patient survival, results were obtained from 47,637 patients transported by helicopter and 111,874 patients transported by ground (based on data from “Association Between Helicopter vs Ground Emergency Medical Services and Survival for Adults
Defective Ultrasound Transducers Among 676 ultrasound transducers tested, 269 were defective with transducer errors (based on data from “High Incidence of Defective Ultrasound Transducers in Use in Routine Clinical Practice,” by Martensson et al., European Journal of Cardiology, Vol. 10). If
Defective Pacemakers Among 8834 cases of heart pacemaker malfunctions, 504 were found to be caused by firmware, which is software programmed into the device (based on data from “Pacemaker and ICD Generator Malfunctions,” by Maisel et al., Journal of the American Medical Association, Vol. 295,
Redundancy in Hospital Generators Hospitals typically require backup generators to provide electricity in the event of a power outage. Assume that emergency backup generators fail 22% of the times when they are needed (based on data from Arshad Mansoor, senior vice president with the Electric Power
Redundancy in Computer Hard Drives It is generally recognized that it is wise to back up computer data. Assume that there is a 3% rate of disk drive failure in a year (based on data from various sources including lifehacker.com).a. If you store all of your computer data on a single hard disk drive,
Testing for Marijuana Use If one of the test subjects is randomly selected, find the probability that the subject used marijuana. Do you think that the result reflects the general population rate of subjects who use marijuana?
Testing for Marijuana Use If one of the test subjects is randomly selected, find the probability that the subject tested positive or did not use marijuana.
Testing for Marijuana Use If one of the test subjects is randomly selected, find the probability that the subject tested negative or used marijuana.
Testing for Marijuana Usea. How many subjects are included in the study?b. How many of the subjects had a true negative result?c. What is the probability that a randomly selected test subject had a true negative result?
Blood Groups and Types If three different people are selected, find the probability that they are all type Rh-.
Blood Groups and Types If three different people are selected, find the probability that they are all Group A.
Blood Groups and Types If one person is selected, find the probability of getting someone who is Group O or Group AB or type Rh+.
Blood Groups and Types If one person is selected, find the probability of getting someone who is Group A or Group B or type Rh-.
Blood Groups and Types If two people are selected, find the probability that they are both Group AB.a. Assume that the selections are made with replacement. Are the events independent?b. Assume that the selections are made without replacement. Are the events independent?
Blood Groups and Types If two people are selected, find the probability that they are both type Rh−.a. Assume that the selections are made with replacement. Are the events independent?b. Assume that the selections are made without replacement. Are the events independent?
Blood Groups and Types If two people are selected, find the probability that they are both Group B.a. Assume that the selections are made with replacement. Are the events independent?b. Assume that the selections are made without replacement. Are the events independent?
Blood Groups and Types If one person is selected, find the probability of getting someone who is type Rh− or Group AB. Are the events of selecting someone who is type Rh−and the event of someone who is Group AB disjoint events?
Blood Groups and Types If one person is selected, find the probability of getting someone who is Group A or type Rh+. Are the events of selecting someone who is Group A and the event of someone who is type Rh+ disjoint events?
Blood Groups and Types If one person is selected, find the probability of getting someone who is not type Rh+.
Blood Groups and Types If one person is selected, find the probability of getting someone who is not Group A.
Sobriety Checkpoint When one of the authors observed a sobriety checkpoint conducted by the Dutchess County Sheriff Department, he saw that 676 drivers were screened and 6 were arrested for driving while intoxicated. Based on those results, we can estimate that P1I2 = 0.000888, where I denotes the
Clinical Test When the drug Viagra (sildenafil citrate) was clinically tested, 117 patients reported headaches and 617 did not. If one of these patients is randomly selected, find the probability of getting one who did not report a headache.
Color Blindness Women have a 0.25% rate of red>green color blindness. If a woman is randomly selected, what is the probability that she does not have red>green color blindness?
LOL A U.S. Cellular survey of smartphone users showed that 26% of respondents answered“yes” when asked if abbreviations (such as LOL) are annoying when texting. What is the probability of randomly selecting a smartphone user and getting a response other than “yes”?
Rule of Complements When randomly selecting an adult, let B represent the event of randomly selecting someone with Group B blood. Write a sentence describing what the rule of complements is telling us: P1B or B2 = 1.
Sample for a Poll There are 15,524,971 adults in Florida. If The Gallup organization randomly selects 1068 adults without replacement, are the selections independent or dependent?If the selections are dependent, can they be treated as being independent for the purposes of calculations?
Notation When randomly selecting adults, let M denote the event of randomly selecting a male and let B denote the event of randomly selecting someone with blue eyes. What does P1M0 B2 represent? Is P1M0 B2 the same as P1B0M2?

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