Applied Biostatistics for the Health Sciences. Richard J. Rossi
variables is a qualitative or quantitative variable. If the variable is a quantitative variable, determine whether it is a discrete or a continuous variable. If the variable is a qualitative variable, determine whether it is a nominal or an ordinal variable.GenderEthnicityDosage of a drug given in whole mgAbdomen circumferenceWhite blood countBody mass index (BMI)Eye colorSurvival time after diagnosis with pancreatic cancerNumber of months since last check upNumber of sexual partners in the last 6 months
6 2.6 Determine whether each of the following qualitative variables is a nominal or an ordinal variable. The values that the variable can take on are listed in parentheses following the name of the variable.Gender (M, F)Size of hospital (small, average, large)Blood type (A, B, AB, O)Radiation dosage (low, medium, high)Use of dietary supplements (yes, no)Fat in diet (low, medium, high)Eat lunch (always, sometimes, never)
7 2.7 The percentages given in Table 2.13 were extracted from a bar chart published in the article “Prevalence of overweight among persons aged 2–19 years, by sex—National Health and Nutrition Examination Survey (NHANES), United States, 1999–2000 through 2003–2004” in the November 17, 2006 issue of the Morbidity and Mortality Weekly Report (MMWR), a Centers for Disease Control and Prevention weekly publication.Table 2.13 Prevalence of Overweight Children According to an Article in the November 17, 2006 Issue of MMWRGenderYear1999–20002001–20022003–2004Male1416.518.2Female13.81416Create a side-by-side bar chart representing the percentages of overweight children for each gender by year.Create a side-by-side bar chart representing the percentages of overweight children for each year by gender.
8 2.8 The percentages in Table 2.14 were extracted from a bar chart published in the article “Percentage distribution of blood pressure categories among adults aged ≥18 years, by race/ethnicity—National Health and Nutrition Examination Survey, United States, 1999–2004” published in the June 22, 2007 issue of the Morbidity and Mortality Weekly Report, a Centers for Disease Control and Prevention weekly publication.Table 2.14 Percentages of Americans in the Blood Pressure Categories as Reported in the June 22, 2007 issue of MMWREthnicityBlood Pressure CategoryNormalPrehypertensionHypertensionHypertensionStage IStage IIMexican American4634128White4637116Black36381610Create a side-by-side bar chart representing the percentages for each of the blood pressure categories by ethnicity category.Create a side-by-side bar chart representing the percentages for each of the blood pressure categories within each ethnicity category.Which ethnicity appears to have the largest percentage in the hypertension stage I and II categories?
9 2.9 The probability density of a continuous variable is given in Figure 2.32. If the points labeled A,B,C,D, and E represent the mode, mean, median, 25th percentile, and the 75th percentile, determine which of the points is theFigure 2.32 The probability distribution of the continuous variable X.median of this distribution.mode of this distribution.mean of this distribution.value that only 25% of the values in the population exceed.value that 50% of the values in the population exceed.value that 75% of the values in the population are less than.
10 2.10 If the 25th and 75th percentiles of the distribution given in Figure 2.32 are 38 and 92, determine the value of the interquartile range.
11 2.11 Use the distribution given in Figure 2.33 representing the hypothetical distribution for the survival times for stage IV pancreatic cancer patients to answer the following questions.Figure 2.33 The distribution for Exercise 2.11.Does the distribution appear to be multi-modal?How many modes does this distribution have?Is this distribution symmetric, long-tailed left, or long-tailed right?What is the value of the mode for this distribution?If the points A and B represent the mean and median, which of these two points is the mean?
12 2.12 What is the most common reason that a variable will have a bimodal distribution?
13 2.13 What is the prevalence of a disease?
14 2.14 How is a percentile different from a population percentage?
15 2.15 How do the mean and median differ?
16 2.16 When are the mean and median equal?
17 2.17 Is themean sensitive to the extreme values in the population?median sensitive to the extreme values in the population?
18 2.18 Suppose the population of 250 doctors at a public hospital has been classified according to the variables Age and Gender and is summarized in the table below.25–4041–5556–70Male546642Female244123Determine the percentage of doctors at this hospital that are female.Determine the percentage of doctors at this hospital that are aged 56 or older.Determine the percentage of doctors at this hospital that are female and aged 41 or older.Determine the percentages of doctors at this hospital in each age group.Determine the age group that the median age falls in.
19 2.19 Describe how the geometric mean (GM) is computed and why it might be used in place of the arithmetic mean.
20 2.20 What are three parameters that measure thetypical values in a population.the spread of a population.
21 2.21 Which of the parametersmeasuring the typical value in a population are not sensitive to the extreme values in a population?measuring the spread of a population are not sensitive to the extreme values in a population?
22 2.22 According to the article “Mean body weight, height, waist circumference, and body mass index among adults: United States, 1999 – 2000 through 2015 – 2016” published in National Health Statistics Report (Fryar, 2018), the estimated mean weight of an adult male in the United States in 2015 – 2016 was 197.8. Suppose the distribution of weights of adult males is a mound shaped distribution with mean µ = 200 and standard deviation σ = 25. Determinethe weight range that approximately 95% of the adult males in the United States in 2015 – 2016 fall in.the coefficient of variation for the weights of adult males in the United States in 2015 – 2016.
23 2.23 For a mound-shaped distribution what is the approximate percentage of the population fallingbetween the values μ−2σ and μ+2σ.above the value μ+3σ.below the value μ−σ.
24 2.24 Which parameter measures the relative spread in a population? How is this parameter computed?
25 2.25 What does it mean whenthe median is much larger than the mean?there is a large distance between the 25th and 75th percentiles?there is a large distance between the 75th and 99th percentiles?
26 2.26 In the article “Mean body weight, height, waist circumference, and body mass index among adults: United States, 1999 – 2000 through 2015 – 2016” published in National Health Statistics Report (Fryar, 2018), the statistics in Table 2.15 were reported for adult females in the United States for 2015 – 2016. Use the information in Table 2.15 to answer the following questions.Table 2.15 The Approximate Means and Standard Deviations for the Variables Weight, Height, and Body Mass Index for Adult Females in the U.S. for 2015 – 2016 for Exercise 2.27VariableMeanStandard DeviationWeight169.8 lbs20 lbsHeight63.6 inches3 inchesBMI29.64Compute the coefficient of variation for the variable weight.Compute the coefficient of variation for the variable height.Compute the coefficient of variation for the variable BMI.
27 2.27 What does it mean when the value of the correlation coefficient for two quantitative variables isρ=−1.ρ = 0.ρ = 1.
28 2.28 What does the correlation coefficient measure?
29 2.29 What are the units of the correlation coefficient?
30 2.30 What does it mean when two events are said to beindependent events?dependent events?
31 2.31 Under what conditions is the probability of the event “A or B” equal to the sum of their respective probabilities?
32 2.32