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biostatistics
Biostatistics For The Biological And Health Sciences 2nd Edition Marc Triola, Mario Triola, Jason Roy - Solutions
3. Notation Evaluate 9C4. What does the result represent?
Permutations , Combinations What is the basic difference between permutations and combinations?
Notation What does the symbol ! represent? Six different patients can be scheduled for X-ray films 6! different ways, so what is the actual number of ways that six people can be scheduled for X-ray films?
Change the Florida population sizes for the three age categories so that they fit the same age distribution as the U.S. population.Next, adjust the corresponding numbers of deaths proportionately. (Use the same Florida mortality rates for the individual age categories, but apply those rates to the
Adjusted Mortality Rate Refer to the data listed in Exercise
Comparing Rates In a recent year, the crude mortality rate of the United States was 8.0(per 1000 population), and the corresponding crude mortality rate for China was 7.4. What is a major problem with comparing the crude mortality rates of the United States and China?
Number of Deaths The number of deaths in the United States has been steadily increasing each year. Does this mean that the health of the nation is declining? Why or why not?
Finding Probability In a recent year in the United States, there were 787,650 deaths due to cardiovascular disease, and the population was 312,799,495.a. Find the crude mortality rate for cardiovascular disease. (This result is sometimes called the cause-specific death rate.)b. Find the probability
Finding Probability The crude death rate for Spain was recently 8.3, and that rate was computed using a multiplier of k = 1000.a. Find the probability that a randomly selected Spaniard died within the year.b. If two Spaniards are randomly selected, find the probability that they both died within
Finding Probability The crude death rate for China was recently 7.4, and that rate was computed using a multiplier of k = 1000.a. Find the probability that a randomly selected Chinese person died within the year.b. If two Chinese people are randomly selected, find the probability that they both
Finding Probability An example in this section involved the crude mortality rate, which was found to be 8.0 persons per 1000 population. Find the probability of randomly selecting someone and getting a person who died within the year. What advantage does the crude mortality rate have over the
Odds Ratio and Relative Risk In a clinical trial of 2103 subjects treated with Nasonex(mometasone), 26 reported headaches. In a control group of 1671 subjects given a placebo, 22 reported headaches. Find the relative risk and odds ratio for the headache data. What do the results suggest about the
Odds Ratio and Relative Risk Find the odds ratio and relative risk for an infection in the group treated with atorvastatin compared to the placebo group. Based on this result, does atorvastatin appear to increase the risk of an infection? Why or why not?
Odds For those who were treated with atorvastatin, find the odds in favor of an infection.Also find the odds in favor of an infection for those given a placebo. Is there much of a difference between these two results?
Number Needed to Treat Calculate the number needed to treat and interpret the result.
Absolute Risk Reductiona. What is the probability of infection in the atorvastatin treatment group?b. What is the probability of infection in the placebo group?c. Find the value of the absolute risk reduction for infection in the placebo group and the atorvastatin treatment group. Write a brief
Odds Ratio Find the odds ratio for headaches in the treatment group compared to the placebo group, then interpret the result. Should Viagra users be concerned about headaches as an adverse reaction?
Relative Risk Find the relative risk of a headache for those in the treatment group compared to those in the placebo group. Interpret the result.
Odds For those in the Viagra treatment group, find the odds in favor of a headache, then find the odds against a headache.
Cotinine in Smokers Refer to the accompanying table summarizing measured amounts of serum cotinine (ng/mL) from a sample of smokers (from Data Set 14 “Passive and Active Smoke” in Appendix B). When nicotine is absorbed by the body, cotinine is produced. How many subjects are included in the
Cotinine in Smokers Refer to the accompanying frequency distribution. What problem is created by using classes of 0–100, 100–200, . . . ?
Relative Frequency Distribution Use percentages to construct the relative frequency distribution corresponding to the accompanying frequency distribution for cotinine amounts.
What’s Wrong? Heights of adult males are known to have a normal distribution, as described in this section. A researcher claims to have randomly selected adult males and measured their heights with the resulting relative frequency distribution as shown here. Identify two major flaws with theses
In Exercises 5–8, identify the class width, class midpoints, and class boundaries f or the given frequency distribution. The frequency distributions are based on real data from Appendix B. Cotinine (NonSmokers Exposed to Smoke in ng/mL) 0-99 Frequency 34 100-199 2 200-299 1 300-399 1 400-499 0
In Exercises 5–8, identify the class width, class midpoints, and class boundaries f or the given frequency distribution. The frequency distributions are based on real data from Appendix B. Brain Volume (cm) 960-1049 1050-1139 1140-1229 1230-1319 Frequency 6 7 3 22 1320-1409 1 1410-1499 1
In Exercises 5–8, identify the class width, class midpoints, and class boundaries f or the given frequency distribution. The frequency distributions are based on real data from Appendix B. Blood Platelet Count of Males Frequency 0-99 1 100-199 51 200-299 90 300-399 10 400-499 0 500-599 0 600-699 1
In Exercises 5–8, identify the class width, class midpoints, and class boundaries f or the given frequency distribution. The frequency distributions are based on real data from Appendix B. Blood Platelet Count of Females Frequency 100-199 25 200-299 92 300-399 28 400-499 0 500-599 2
Cotinine Determine whether the frequency distribution given in Exercise 5 is approximately a normal distribution. Explain.
Brain Volume Refer to the frequency distribution given in Exercise 6 and ignore the given frequencies.Assume that the first three frequencies are 1, 3, and 6, respectively. Assuming that the distribution of the 20 sample values is a normal distribution, identify the remaining three frequencies.
Normal Distribution Refer to the frequency distribution given in Exercise 7 and ignore the given frequencies. Assume that the first three frequencies are 2, 12, and 18, respectively.Assuming that the distribution of the 153 sample values is a normal distribution, identify the remaining four
Do the pulse rates of males appear to have a normal distribution?14. Pulse Rates of Females Refer to Data Set 1 “Body Data” in Appendix B and use the pulse rates (beats per minute) of females. Begin with a lower class limit of 30 and use a class width of
Do the pulse rates of females appear to have a normal distribution?15. Lead and IQ Refer to Data Set 8 “IQ and Lead” in Appendix B and use the verbal IQ scores of the low lead group. Begin with a lower class limit of 50 and use a class width of 10.Do these IQ scores appear to be normally
Cotinine Construct one table (similar to Table 29 on page 48) that includes relative frequencies based on the frequency distributions from Exercise 1 (smokers) and Exercise 5 (nonsmokers exposed to smoke), and then compare them. Are there notable differences?
Blood Platelet Counts Construct one table (similar to Table 29 on page 48) that includes relative frequencies based on the frequency distributions from Exercises 7 and 8, and then compare them. Are there notable differences?25. Exercise 5 Cumulative Frequency Distributions. In Exercises 25 and 26,
Interpreting Effects of Outliers Exercise 5 in this section involved cotinine levels of nonsmokers who were exposed to tobacco smoke. (See the middle column in Data Set 14“Passive and Active Smoke” in Appendix B.)a. Identify any outliers.b. After adding another value of 999 to the cotinine
Body Temperatures Listed below are body temperatures (°F) of healthy adults. Why is it that a graph of these data would not be very effective in helping us understand the data?98.6 98.6 98.0 98.0 99.0 98.4 98.4 98.4 98.4 98.6
Voluntary Response Data If we have a large voluntary response sample consisting of weights of subjects who chose to respond to a survey posted on the Internet, can a graph help to overcome the deficiency of having a voluntary response sample?
Ethics There are data showing that smoking is detrimental to good health. Given that people could be helped and lives could be saved by reducing smoking, is it ethical to graph the data in a way that is misleading by exaggerating the health risks of smoking?
CVDOT Section 21 introduced important characteristics of data summarized by the acronym CVDOT. What characteristics do those letters represent, and which graph does the best job of giving us insight into the last of those characteristics?
Pulse Rates Listed below are pulse rates (beats per minute) of females selected from Data Set 1 “Body Data” in Appendix B. All of those pulse rates are even numbers. Is there a pulse rate that appears to be an outlier? What is its value?80 94 58 66 56 82 78 86 88 56 36 66 84 76 78 64 66 78 60 64
Diastolic Blood Pressure Listed below are diastolic blood pressure measurements(mm Hg) of females selected from Data Set 1 “Body Data” in Appendix B. All of the values are even numbers. Are there any outliers? If so, identify their values.62 70 72 88 70 66 68 70 82 74 90 62 70 76 90 86 60 78 82
Pulse Rates Refer to the data listed in Exercise
How are the data sorted in the stemplot?
Diastolic Blood Pressure Refer to the data listed in Exercise
Identify the two values that are closest to the middle when the data are sorted in order from lowest to highest. (These values are often used to find the median, which is defined in Section 31.)
Triplets Listed below are the numbers of triplets born in the United States each year beginning with 1995. Is there a trend?4551 5298 6148 6919 6742 6742 6885 6898 7110 6750 6208 6118 5967 5877 5905 5153 5137 4598
Drunk Driving Fatalities Listed below are annual fatality rates (per 100,000 population)from drunk driving. The first entry represents the year 1991. Is there a trend? Any explanation?6.3 5.5 5.3 5.1 5.1 5.1 4.8 4.6 4.6 4.7 4.7 4.7 4.5 4.5 4.6 4.5 4.3 3.9 3.5 3.3 3.2 3.3
Journal Retractions In a study of retractions in biomedical journals, 436 were due to error, 201 were due to plagiarism, 888 were due to fraud, 291 were duplications of publications, and 287 had other causes (based on data from “Misconduct Accounts for the Majority of Retracted Scientific
Getting a Job In a survey, subjects seeking a job were asked to whom they send a thankyou note after having a job interview. Results were as follows: 40 said only the person they spent the most time with, 40 said only the most seniorlevel person, 396 said everyone that they met, 15 said the person
Journal Retractions Use the data from Exercise 11 “Journal Retractions.”
Getting a Job Use the data from Exercise 12 “Getting a Job.”
Pulse Rates of Males Use the frequency distribution for the pulse rates of males from Exercise 13 in Section 21 on page 49 to construct a frequency polygon. Comment on the shape of the distribution.
Pulse Rates of Females Use the frequency distribution for the pulse rates of females from Exercise 14 in Section 21 on page 49 to construct a frequency polygon. Comment on the shape of the distribution.17.Self-Driving Vehicles In a survey of adults, subjects were asked if they felt comfortable
Cost of Giving Birth According to the Agency for Healthcare Research and Quality Healthcare Cost and Utilization Project, the typical cost of a Csection baby delivery is $4500, and the typical cost of a vaginal delivery is $2600. See the accompanying illustration.
Linear Correlation In this section we use r to denote the value of the linear correlation coefficient.Why do we refer to this correlation coefficient as being linear?
Causation A study has shown that there is a correlation between body weight and blood pressure. Higher body weights are associated with higher blood pressure levels. Can we conclude that gaining weight is a cause of increased blood pressure?
Scatterplot What is a scatterplot and how does it help us?
Estimating r For each of the following, estimate the value of the linear correlation coefficient r for the given paired data obtained from 50 randomly selected adults.a. Their heights are measured in inches (x) and those same heights are recorded in centimeters (y).b. Their IQ scores (x) are
Bear Measurements The table lists chest sizes (distance around chest in inches) and weights (pounds) of anesthetized bears that were measured (from Data Set 11 in Appendix B).Chest (in.) 26 45 54 49 35 41 41 Weight (lb) 80 344 416 348 166 220 262
Body Temperatures The table lists body temperatures (°F) of seven healthy adults at 8 AM on one day and at 8 AM on the following day (from Data Set 2 “Body Temperatures” in Appendix B).Day 1 98.6 97.4 98.2 98.2 98.2 96.6 97.4 Day 2 97.8 97.0 97.0 96.6 97.0 96.8 96.6
Heights of Fathers and Sons The table lists heights (in.) of fathers and the heights (in.) of their first sons (from Francis Galton).Height of father (in.) 73.0 75.5 75.0 75.0 75.0 74.0 74.0 73.0 73.0 78.5 Height of first son (in.) 74.0 73.5 71.0 70.5 72.0 76.5 74.0 71.0 72.0 73.2
Using the data from Exercise 5 “Brain Volume and IQ,” the linear correlation coefficient is r = 0.127.10. Using the data from Exercise 6 “Bear Measurements,” the linear correlation coefficient is r = 0.980.
Using the data from Exercise 7 “Body Temperatures,” the linear correlation coefficient is r = 0.520.
Using the data from Exercise 8 “Heights of Fathers and Sons,” the linear correlation coefficient is r = -0.017.
BAC When constructing a table representing the frequency distribution of blood alcohol content (g>dL) of drunk drivers involved in fatal car crashes, the first two classes of a frequency distribution are 0.08 – 0.11 and 0.12 – 0.15. What is the class width?
BAC Using the same first two classes from Exercise 1, identify the class boundaries of the first class.
BAC The first class described in Exercise 1 has a frequency of
If you know only the class limits given in Exercise 1 and the frequency of 36, can you identify the original 36 data values?
BAC A stemplot is created from the ages of drunk drivers involved in fatal car crashes and the first row is 1 | 67889. Identify the values represented by that row.
Reaction Times A large sample is randomly selected from a normally distributed population of reaction times, and a histogram is constructed from a frequency distribution. What is the shape of the histogram?
Tylenol In testing samples of regular Tylenol pills to verify that they have close to the desired amount of 325 mg of acetaminophen, which important characteristic of data is missing from this list: center, distribution, outliers, changes over time?
Tylenol A quality control manager wants to monitor the production of regular Tylenol pills to be sure that the mean amount of acetaminophen does not change over time. Which of the following graphs is most helpful for that purpose: histogram, Pareto chart, pie chart, scatterplot, timeseries graph,
Blood Pressure In an investigation of the relationship between systolic blood pressure and diastolic blood pressure, which of the following graphs is most helpful: histogram; pie chart;scatterplot; stemplot; dotplot?
Blood Pressure Thing The W. A. Baum Company manufactures sphygmomanometers used to measure blood pressure. Quality control managers at such companies monitor defects and identify various causes, including worn machinery, human error, bad supplies, and packaging mistreatment. Which of the following
Frequency Distribution and Histogram What is the basic difference between a frequency distribution and a histogram?
Frequency Distribution of Body Temperatures Construct a frequency distribution of the 20 body temperatures 1 F2 listed below. (These data are from Data Set 2 “Body Temperatures”in Appendix B.) Use a class width of 0.5 F and a starting value of 97.0 F.97.1 97.2 97.5 97.6 97.6 97.8 98.0 98.0 98.2
Histogram of Body Temperatures Construct the histogram that corresponds to the frequency distribution from Exercise
Use class midpoint values for the horizontal scale. Does the histogram suggest that the data are from a population having a normal distribution? Why or why not?
Dotplot of Body Temperatures Construct a dotplot of the body temperatures listed in Exercise
Which does a better job of illustrating the distribution of the data: the histogram from Exercise 2 or the dotplot?
Stemplot of Body Temperatures Construct a stemplot of the body temperatures listed in Exercise
Are there any outliers?
Bears Listed below are the neck sizes (in.) and weights (lb) of bears (from Data Set 11“Bear Measurements” in Appendix B). Construct a scatterplot. Based on the graph, does there appear to be a relationship between neck sizes and weights of bears?Neck Size (in.) 16 28 31 31.5 22 21 26.5 27 20
Monitoring Weighta. After collecting the average (mean) weight of adult males in the United States for each of the most recent 100 years, we want to construct the graph that is most appropriate for these data.Which graph is best?b. After collecting the average (mean) weight and height of males for
Medical School Enrollees The accompanying graph illustrates male and female enrollees in U.S. medical schools in a recent year. What is wrong with the graph?
Hygiene Listed below are times (minutes) spent on hygiene and grooming in the morning by randomly selected subjects (based on data from a Svenska Cellulosa Aktiebolaget survey).Construct a table representing the frequency distribution. Use the classes 0–9, 10–19, and so on.0 5 12 15 15 20 22 24
Hygiene Histogram Use the frequency distribution from Exercise 1 to construct a histogram.Use class midpoint values for the horizontal scale. Based on the result, do the data appear to be from a population with a normal distribution? Explain.
Hygiene Stemplot Use the data from Exercise 1 to construct a stemplot.
Analysis of Last Digits Use the data from Exercise 1 and construct a frequency distribution of the last digits of the grooming times. What does the result suggest about the grooming times?
Hygiene Refer to the grooming times given in Exercise 1.a. What is the level of measurement of those times? (nominal, ordinal, interval, ratio)b. Are the exact unrounded grooming times discrete data or continuous data?c. Are the grooming times categorical data?d. The average (mean) of the grooming
Mother , Daughter Heights Refer to the following list of heights of mothers and the heights of their first daughters (from Data Set 6 “Family Heights” in Appendix B). What issue would be investigated with these data? Construct the best graph for investigating that issue. What does that graph
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