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biostatistics
Basic Biostatistics Statistics For Public Health Practice 2nd Edition B.Burt Gerstman - Solutions
Poverty in eastern states, 2000. Table 3.5 lists the percentage of people living below the poverty line in the 26 states east of the Mississippi River for the year 2000. Make a stemplot of these values.After creating the plot, describe the distribution’s shape, location, and spread. Are there any
Hospitalization. Table 3.6 lists lengths of stays (days) for a sample 25 patients.(a) Create a stemplot with single stem values for these data. (Use an axis multiplier of ×10).(b) Create a stemplot with split stem values.(c) Which of the stemplots do you prefer?(d) Describe in plain language the
Leaves on a common stem. For each of the following comparisons, plot the data as back-to-back stemplots on a common stem. Then, compare group locations and spreads.(a) Comparison A(b) Comparison B(c) Comparison C
Cholesterol comparison. Table 3.7 lists plasma cholesterol levels(mmol/m3) in two independent groups. Plot these data on a common stem. Then, compare group locations and spreads.
Hospital stay duration. In Exercise 3.2, you created a stemplot of lengths of hospital stays for 25 patients. Table 3.6 lists the data.(a) Construct a frequency table for these data using 5-day class intervals. Include columns for the frequency counts, relative frequencies, and cumulative
Name three general characteristics of distributions.
Select the best response: An asymmetrical distribution with a long right tail (toward the higher numbers) is said to have ___________ skew.(a) a positive(b) a negative(c) no
Select the best answer: An asymmetrical distribution with a long left tail is said to have ___________ skew.(a) a positive(b) a negative(c) no
What term refers to the number of peaks in a distribution?
What is a deviation from the overall pattern of a distribution?
Select the best response: This refers to a flat curve with thick tails.(a) platykurtotic(b) mesokurtotic(c) leptokurtotic
Select the best response: This refers to the “peak” of a distribution.(a) mean(b) median(c) mode
What refers to a distribution with two peaks?(a) nonmodal(b) unimodal(c) bimodal
The two most common measures of central location are the ___________ and ___________.
What statistic identifies the gravitational center of a distribution?
What statistic identifies the value that is greater than or equal to 50%of the other data points in a distribution?
Fill in the blank: The median is located at a depth of ___________ in the ordered array (where n is the sample size).
How many leaves are there on a stemplot?
What is the purpose of a stem (axis) multiplier?
What is another technical term for a count?
What is another technical term for a proportion?
What is the proportion of values at or below a specified value?
Why are end-point conventions needed when constructing frequency tables with class intervals?
True or false? Histograms are used to display frequencies for categorical data.
Outpatient wait time. Waiting times (minutes) for 25 patients at a public health clinic areg:(a) Create a stemplot of these data. Describe the distribution’s shape, location, and spread.(b) From your stemplot, create a frequency table with counts, relative frequencies, and cumulative relative
Body weight expressed as a percentage of ideal. Body weights of 18 diabetics expressed as a percentage of ideal (defined as body weight÷ ideal body weight × 100) are shown here.h Construct a stem-andleaf plot of these data and interpret your findings.
Docs’ kids. The numbers of children of 24 physicians who work at a particular clinic are shown here.i Create a stemplot with these data.Consider its shape, location, and spread. What percentage of physicians at this clinic have less than three children?
Seizures following bacterial meningitis. A study examined the induction time between bacterial meningitis and the onset of seizures in 13 cases (months). Data are shown here.j Construct a stemplot of these data and describe what you see. [Suggestion: Use a stem multiplier of ×10 so that the value
Surgical times. Durations of surgeries (hours) for 14 patients receiving artificial hearts are shown here.k Create a stem plot of these data. Describe the distribution. Are there any outliers?
U.S. Hispanic population. Table 3.9 lists the percent of residents in the 50 states who identified themselves in the 2000 census as Spanish, Hispanic, or Latino. Create a stemplot of these data using single stem values and an axis multiplier of ×10. Then create a stemplot using double-split stem
Low birth weight rates. A birth weight of less than 2500 grams(about 5.5 pounds) qualifies as “low birth weight” according to international standards. Table 3.10 lists low birth weight rates (per 100 births) by country for the year 1991 in 109 countries.(a) Explore these data with a stemplot.
Air samples. An environmental study looked at suspended particulate matter in air samples (µg/m3) at two different sites. Data are listed here.l Construct side-by-side stemplots to compare the two sites.
Low birth weight rates. Create a frequency table for the low birth weight data in Table 3.10. Use two-unit class intervals to construct your table, starting with the interval 0–1. Include frequency counts, relative frequencies, and cumulative frequencies in your table.
Practicing docs. The Health United States series published by the National Center for Health Statistics each year tracks trends in health and health care in the United States. Table 3.11 is derived from a part of Table 104 in Health United States 2006. This table lists the number of practicing
Health insurance. Table 3.12 lists the percentage of people without health insurance in the 50 states and the District of Columbia for the year 2004. In addition to being listed in Table 3.12, data are also stored on the companion website in file INC-POV-HLTHINS.* as the variable NOINS (no
Cancer treatment. A new cancer treatment uses genetically engineered white blood cells to recognize and destroy cancer cells.Counts of activated immune cells in 11 patients are as follows: {27, 7, 0, 215, 20, 700, 13, 510, 34, 86, 108} (data are fictitious). Make a stemplot of the data. Describe
Gravitational center. This exercise will demonstrate how the mean is the balancing point of a set of numbers.(a) Distribution A. The values 1 and 5 are marked as “Xs” on the following number line. Calculate the mean and mark its location on the number line.(b) Distribution B. The values 1, 5,
Visualizing the mean. Consider these eight data points:A stemplot of the data looks like this:Visually estimate (“eyeball”) the balancing point of the distribution;then calculate the distribution’s mean. How well did you do with your “eyeball” estimate?
More visualization. Figure 4.3 contains three stemplots. Stemplot A represents ages (years) of participants in a childhood health survey (n= 322). Stemplot B represents body weights of students in a class (n= 53). Stemplot C represents coliform levels in water samples (n =25). Look at each of these
Outside? The following stemplot has 18 observations. Prove that the value 152 in this data set is an outside value. Then draw the boxplot for the data.
Seizures following bacterial meningitis. In Exercise 4.4, you calculated the mean and median of induction times in 13 seizures cases. Data were {0.10, 0.25, 0.50, 4, 12, 12, 24, 24, 31, 36, 42, 55, 96} months. Now construct a boxplot for these data. Are there any outside values in this data set?
Standard deviation for site 1. Use a step-by-step approach to calculate the standard deviation of the data for site 1 listed in Table 4.2. Compare this standard deviation to that of the data from site 2 (s2= 2.88μg/m3). How does this numerical comparison relate to what you see in Figure 4.5?
Standard deviation via technology. In practice, we normally use statistical calculators or computers to calculate standard deviations.Using your statistical calculator or computer, calculate the standard deviations and variances for the air samples data originally presented in Table 4.2. Make
Heart rate. An individual with an irregular heartbeat is given a medication to stabilize his condition. Heart rates (beats per minute)before and after treatment are shown here.h Determine the means and standard deviations before and after treatment. Did the drug work?
Units of measure change numeric values of a standard deviation.Calculate the standard deviations of the batches of numbers here.Which batch has the greatest variability?This exercise demonstrates a potential problem when comparing standard deviations for variables using different units of
Test scores with mean 100 and standard deviation 10. Test scores have a Normal distribution with a mean of 100 and standard deviation of 10. What percentage of scores falls in the range 80 to 120? Explain.
Which statistics? Which measures of central location and spread would you use to describe each of the data sets depicted in Figure 4.3?
Effect of removing an outlier.j Exercise 4.6 looked at months between bacterial meningitis and the onset of seizures in 13 cases.Data were {0.10, 0.25, 0.50, 4, 12, 12, 24, 24, 31, 36, 42, 55, 96}.(a) Calculate the mean and standard deviation for these data.(b) Calculate the median and IQR.(c)
In statistical notation, how does x differ from X?
Name three measures of central location.
Name four measures of spread.
A sample mean is used to “predict” three things. List these things.
What does it mean when we say that a statistic is robust?
Which is more robust: the mean or the median?
Which is more robust: the standard deviation or the inter-quartile range?
Where is the median of a data set located?
Why is the sample range a poor measure of spread?
Provide two synonyms for Q1 (quartile 1).
Provide two synonyms for Q3 (quartile 3).
What is a hinge spread?
List the elements of a 5-point summary.
When determining the quartiles by Tukey’s hinge method and n is odd, do you include the median in the low- and high-groups when splitting the data set?
True or false: There is a universally accepted way to interpolate quartiles in datasets.
How do you determine whether a data point is an outside value?
What is an upper inside value? What is a lower inside value?
What is a deviation?
What statistic is the sum of squared deviations divided by n − 1?
What statistic is the square root of a variance?
What is the standard deviation of this data set: {5, 5, 5, 5}?[Calculations not required.]
What rule says “at least 75% of the data points will always fall within two standard deviation of the mean”?
Select the best response: When do 95% of the values fall within 2 standard deviations of the mean?(a) always(b) when the distribution is symmetrical(c) only when the distribution is normal
Why do we lose one degree of freedom when calculating the sample standard deviation?
Leaves on stems. Calculate the mean and standard deviation of each group depicted in each of the side-by-side stemplots in this problem.Discuss how these statistics relate to what you see.(a) Comparison A(b) Comparison B(c) Comparison C
Irish healthcare websites. Table
in the prior chapter considered the reading levels of Irish healthcare websites. Here’s a reissue of the stemplot for the data:(a) Which measure of location and spread would you use to describe this distribution?(b) Calculate the five-point summary for the distribution.(c) Does this data set have
Health insurance by state. Table 4.3 lists the percent of people without health insurance by state.(a) Calculate the mean and median of these data. Compare these statistics. What does this tell you about the shape of the distribution?(b) Determine the five-point summary for the data.(c) Are there
Skinfold thickness. Skinfold thickness over the triceps muscle in the arm is an anthropometric measure that varies with states of health.Table 4.4 lists skinfold measurements at the midpoint of the triceps in five men with chronic lung disease and six comparably aged controls. Compare the groups
What would you report? A small data set (n = 9) has the following values {3.5, 8.1, 7.4, 4.0, 0.7, 4.9, 8.4, 7.0, 5.5}. Plot the data as a stemplot and then report an appropriate measures of central location and spread for the data.
and s by hand. To assess the air quality in a surgical suite, the presence of colony-forming spores per cubic meter of air is measured on three successive days. The results are as follows: {12, 24, 30}(data are fictitious).(a) Calculate the mean and standard deviation for these data by hand, using
Practicing docs (side-by-side boxplots). In Exercise 3.15, you used side-by-side stemplots to compare the number of practicing medical doctors per 10,000 in the fifty United States and District of Columbia for the years 1975 and 2004. Let us now create side-by-side boxplots for the same purpose.
Practicing docs (means and standard deviations). Recall the data set used in Exercises 3.15 and 4.21. Download the data set(HEALTHUNITEDSTATES2006TABLE104.*) from the companion website.Then, compute the mean and standard deviation for the 1975 and 2004 data using a statistical program of your
Melanoma treatment. A study by Morgan and coworkers used genetically modified white blood cells to treat patients with melanoma who had not responded to standard treatments.k In patients in whom the cells were cultured ex vivo for an extended period of time (cohort 1), the cell doubling times were
Explaining probability. A patient newly diagnosed with a serious ailment is told he has a 60% probability of surviving 5 or more years.Let’s assume this statement is accurate. Explain the meaning of this statement to someone with no statistical background in terms he or she will understand.
Roll a die. A standard die has six faces: one with one spot on it, one with two spots, and so on. We can say that the chance the die lands on “one” is 1 in 6. How would you design an experiment to confirm this statement?
February birthdays. What is the probability of being born on …(a) February 28?(b) February 29?(c) February 28 or 29?
Childhood leukemia. Compilation of results from a clinical trial reveals that 475 of 601 cases survive at least 5 years after diagnosis.Based on this information, estimate the probability of survival; then explain why this is only an estimate of the probability and is not the“true” probability
N = 26. Suppose a population has 26 members identified with the letters A through Z.(a) You select one individual at random from this population. What is the probability of selecting individual A?(b) Assume person A gets selected on an initial draw, you replace person A into the sampling frame, and
Random eights. Chapter 2 introduced Table A, our table of random digits. This table was produced so that each digit 0 through 9 has an equal probability of appearing at any point in the table.(a) Each row has 50 digits. How many 8s do you expect to encounter in the first two rows of the table?(b)
Personal expressions of probability. The probability associated with a proposition can be used to quantify the confidence in a judgment.At one extreme, a probability statement of 0 represents the personal belief that the proposition can never happen. At the other extreme, a probability statement of
Natality. Table 5.4 is a pmf for the age of mothers of newborns in the United States.(a) If we select a birth at random, what is the probability the mother is 19 years of age or younger?(b) What is the probability she is 30 years of age or older?(c) What is the expected age of the mother at birth?
Lottery. A lottery offers a grand prize of $10 million. The probability of winning this grand prize is 1 in 55 million (≈1.8 × 10−8). There are no other prizes, so the probability of winning nothing = 1 − (1.8 ×10−8) = 0.999999982. Table 5.5 shows the probability mass function for the
U.S. Census. Table 5.6 shows the proportions of individuals crossclassified according to two race/ethnic criteria: Hispanic/not Hispanic and Asian/Black/White/other. (The 2010 U.S. census allowed individuals to identify their ethnicity according to more than one criterion.) What is the probability
Uniform (0,1) pdf. Figure 5.7 depicts the probability density function for the random number spinner for values between 0.0 and 1.0. This is the uniform probability density function for the range 0 to 1, denoted X, ~ uniform(0, 1). Use geometry to determine the following probabilities on this
Uniform (0,1) pdf, continued. Again consider the uniform probability density function for the range 0.0 to 1.0. Find the following probabilities.(a) Pr(X ≥ 0.6)(b) Pr(X ≤ 0.6)
The sum of two uniform (0, 1) random variables. Figure 5.8 depicts the pdf for the sum of two uniform (0, 1) random variables.(a) What is the probability of observing a value for this random variable that is less than 1?(b) Use geometry to find the probability of a value that is less than 0.5.(c)
Bound for Glory. Most people have an intuitive sense of how probabilities work. Here is a passage from Woody Guthrie’s autobiography Bound for Gloryd that demonstrates clear probabilistic reasoning:A kid named Bud run the gambling wheel. It was an old lopsided bicycle wheel that he had found in
Fill in the blank: The probability of an event is its relative ___________ in an infinitely long series of repetitions.
What is a numerical quantity that takes on different values depending on chance?
The two types of random variables are continuous and ___________.
What type of random variable takes on a countable set of possible outcomes?
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