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biostatistics
Biostatistics For The Biological And Health Sciences 2nd Edition Marc Triola, Mario Triola, Jason Roy - Solutions
What type of random variable forms an unbroken chain of possible outcomes?
Select the best response: This is a mathematical function that assigns probabilities for discrete random variables.(a) sample space(b) probability mass function (pmf)(c) probability density function (pdf)
Select the best response: This is a mathematical function that assigns probabilities for a continuous random variable.(a) sample space(b) probability mass function (pmf)(c) probability density function (pdf)
Select the best response: This is a description of all possible outcomes for a random variable.(a) an event(b) the sample space(c) probability
What is the complement of an event?
List the first four elementary properties of probability presented in this text.
What symbol is used to denote the expected value of a pmf or pdf?
What symbol is used to denote the variance of a pmf or pdf?
What symbol is used to denote the standard deviation of a pmf or pdf?
What does AUC stand for?
Select the best response: The area under the curve of pmfs and pdfs corresponds to ___________.(a) events(b) probabilities(c) cumulative probabilities
Select the best response: The area under a pmf or pdf curve to the left of a point corresponds to its ___________.(a) event(b) probability(c) cumulative probability
Select the best response: The total area under a pmf or pdf curve is always equal to(a) 0(b) 1(c) something between 0 and 1
Select the best response: The probability of landing on any exact value on a pdf curve is always equal to(a) 0(b) 1(c) something between 0 and 1
Uniform distribution of highway accidents. Accidents occur along a 5-mile stretch of highway at a uniform rate. The following “curve”depicts the probability density function for accidents along this stretch:Notice that this “curve” demonstrates the first two basic properties of probability
Nonuniform distribution of highway accidents. There is a particularly treacherous stretch on a 3-mile stretch of a different highway between miles 1 and 2 where accidents occur at twice the rate of the other two miles.(a) Sketch the probability density curve that describes the occurrence of
Bound for Glory (variance). Exercise 5.14 addressed the probability density function of a crude roulette wheel with values 1 to 60. A bet of a dollar pays $10 on a winning spin. Let X represent the payoff on a one-dollar wager. The probability mass function of potential winnings is therefore:X
The sum of two uniform (0, 1) random variables (µ and median).Exercise 5.13 addressed the pdf for the sum of two uniform (0,1)random numbers (Figure 5.8).(a) The expected value μ of a pdf can be visualized as its gravitational center—the point where the pdf would balance if put on a fulcrum.
The sum of two uniform (0, 1) random variables. Let X represent the sum of these two uniformly distributed (0,1) random variables, as shown in Figure 5.8. Recall that the area of a triangle = ½hb. Use Figure 5.8 to determine:(a) Pr(X < 1).(b) Pr(X > 1.5).(c) Pr(1 < X < 1.5).
Comparing Birth Weights The birth weights of a sample of males have a mean of 3273 g and a standard deviation of 660 g. The birth weights of a sample of females have a mean of 3037 g and a standard deviation of 706 g (based on Data Set 3 “Births” in Appendix B). When considered among members of
ER Codes In an analysis of activities that resulted in brain injuries presenting at hospital emergency rooms (ERs), the following activities were identified by the code shown in parentheses:bicycling (12); football (14); playground (22); basketball (27); swimming (40). Find the mean of 12, 14, 22,
z Score Using the sample data from Exercise 1, find the z score corresponding to the eye height of 1642 mm. Is that eye height significantly low or significantly high? Why or why not?
Ergonomics When designing an eye-recognition security device, engineers must consider the eye heights of standing women. (It’s easy for men to bend lower, but it’s more difficult for women to rise higher.) Listed below are the eye heights (in millimeters) obtained from a simple random sample of
Sleep Notation Consider a sample of sleep times taken from the population of all adults living in Alaska. Identify the symbols used for the sample mean, population mean, sample standard deviation, population standard deviation, sample variance, and the population variance.
Estimating s A large sample of sleep times includes values ranging from a low of 4 hours to a high of 10 hours. Use the range rule of thumb to estimate the standard deviation.
Sleep 5-Number Summary For a sample of 100 sleep times, give the names of the values that constitute the 5-number summary. (The actual values can’t be identified; just give the names of those values.)
Sleep Q3 For a sample of 80 sleep times, approximately how many of those times are less than Q3?
Sleep z Score A larger sample of 50 sleep times (hours) has a mean of 6.3 hours and a standard deviation of 1.4 hours. What is the z score for a sleep time of 5 hours?
Sleep Outlier If the sleep time of 0 hours is included with the sample data given in Exercise 1, is it an outlier? Why or why not?
Sleep Variance The standard deviation of the sample values in Exercise 1 is 1.3 hours.What is the variance (including units)?
Sleep Mode What is the mode of the sample values listed in Exercise 1?
Sleep Median What is the median of the sample values listed in Exercise 1?
Sleep Mean As part of the National Health and Nutrition Examination Survey, subjects were asked how long they slept the preceding night and the following times (hours) were reported:8, 7, 5, 7, 4, 7, 6, 7, 8, 8, 8, 6. Find the mean.
Radiation in Baby Teeth Listed below are amounts of strontium-90 (in millibecquerels, or mBq) in a simple random sample of baby teeth obtained from Pennsylvania residents born after 1979 (based on data from “An Unexpected Rise in Strontium-90 in U.S. Deciduous Teeth in the 1990s,” by Mangano
Cell Phone Radiation Listed below are the measured radiation absorption rates (in W>kg) corresponding to these cell phones: iPhone 5S, BlackBerry Z30, Sanyo Vero, Optimus V, Droid Razr, Nokia N97, Samsung Vibrant, Sony Z750a, Kyocera Kona, LG G2, and Virgin Mobile Supreme. The data are from the
Foot Lengths The following are the foot lengths (cm) of 19 males (from Data Set 7 “Foot and Height” in Appendix B).25.1 25.4 25.7 25.9 26.4 26.7 26.7 26.7 26.8 27.5 27.8 27.9 27.9 28.1 28.6 28.7 28.8 29.2 29.2
P85 In Exercises 21–28, use the same list of bear lengths (in.) given for Exercises 17–20. Find the indicated percentile or quartile.
P25 In Exercises 21–28, use the same list of bear lengths (in.) given for Exercises 17–20. Find the indicated percentile or quartile.
P75 In Exercises 21–28, use the same list of bear lengths (in.) given for Exercises 17–20. Find the indicated percentile or quartile.
P50 In Exercises 21–28, use the same list of bear lengths (in.) given for Exercises 17–20. Find the indicated percentile or quartile.
P40 In Exercises 21–28, use the same list of bear lengths (in.) given for Exercises 17–20. Find the indicated percentile or quartile.
Q3 In Exercises 21–28, use the same list of bear lengths (in.) given for Exercises 17–20. Find the indicated percentile or quartile.
Q1 In Exercises 21–28, use the same list of bear lengths (in.) given for Exercises 17–20. Find the indicated percentile or quartile.
P60 In Exercises 21–28, use the same list of bear lengths (in.) given for Exercises 17–20. Find the indicated percentile or quartile.
58.0 in. Percentiles. In Exercises 17–20, use the following lengths (inches) of bears (from Data Set 11 “Bear Measurements” in Appendix B). Find the percentile corresponding to the given length.36.0 37.0 40.0 40.0 41.0 43.0 43.5 46.0 46.0 47.0 48.0 48.0 49.0 50.0 52.0 52.5 53.0 53.0 54.0 57.3
70.0 in. Percentiles. In Exercises 17–20, use the following lengths (inches) of bears (from Data Set 11 “Bear Measurements” in Appendix B). Find the percentile corresponding to the given length.36.0 37.0 40.0 40.0 41.0 43.0 43.5 46.0 46.0 47.0 48.0 48.0 49.0 50.0 52.0 52.5 53.0 53.0 54.0 57.3
47.0 in. Percentiles. In Exercises 17–20, use the following lengths (inches) of bears (from Data Set 11 “Bear Measurements” in Appendix B). Find the percentile corresponding to the given length.36.0 37.0 40.0 40.0 41.0 43.0 43.5 46.0 46.0 47.0 48.0 48.0 49.0 50.0 52.0 52.5 53.0 53.0 54.0 57.3
61.0 in. Percentiles. In Exercises 17–20, use the following lengths (inches) of bears (from Data Set 11 “Bear Measurements” in Appendix B). Find the percentile corresponding to the given length.36.0 37.0 40.0 40.0 41.0 43.0 43.5 46.0 46.0 47.0 48.0 48.0 49.0 50.0 52.0 52.5 53.0 53.0 54.0 57.3
Oscars In the 87th Academy Awards, Eddie Redmayne won for best actor at the age of 33 and Julianne Moore won for best actress at the age of 54. For all best actors, the mean age is 44.1 years and the standard deviation is 8.9 years. For all best actresses, the mean age is 36.2 years and the
Birth Weights Based on Data Set 3 “Births” in Appendix B, newborn males have weights with a mean of 3272.8 g and a standard deviation of 660.2 g. Newborn females have weights with a mean of 3037.1 g and a standard deviation of 706.3 g. Who has the weight that is more extreme relative to the
Red Blood Cell Counts Based on Data Set 1 “Body Data” in Appendix B, males have red blood cell counts with a mean of 4.719 and a standard deviation of 0.490, while females have red blood cell counts with a mean of 4.349 and a standard deviation of 0.402. Who has the higher count relative to the
Tallest and Shortest Men The tallest living man at the time of this writing is Sultan Kosen, who has a height of 251 cm. The shortest living man is Chandra Bahadur Dangi, who has a height of 54.6 cm. Heights of men have a mean of 174.12 cm and a standard deviation of 7.10 cm. Which of these two men
Ergonomics in Aircraft Seats In the process of designing aircraft seats, it was found that men have hip breadths with a mean of 36.6 cm and a standard deviation of 2.5 cm (based on anthropometric survey data from Gordon, Clauser, et al.). Identify the hip breadths of men that are significantly low
Birth Weights Data Set 3 “Births” lists birth weights (g) of 400 babies. Those weights have a mean of 3152.0 g and a standard deviation of 693.4 g. Identify birth weights that are significantly low or significantly high.
MCAT In a recent year, scores on the MCAT had a mean of 25.2 and a standard deviation of 6.4. Identify the MCAT scores that are significantly low or significantly high.
ACT The ACT test is used to assess readiness for college. In a recent year, the mean ACT score was 21.1 and the standard deviation was 5.1. Identify the ACT scores that are significantly low or significantly high.
Body Temperatures For the body temperatures at 12 AM on day 2 (listed in Data Set 2“Body Temperatures” in Appendix B), the mean is 98.20F, the standard deviation is 0.62F, and Q3 = 98.60F.a. What is the difference between Q3 and the mean?b. How many standard deviations is that [the
Body Temperatures For the body temperatures at 12 AM on day 2 (listed in Data Set 2“Body Temperatures” in Appendix B), the mean is 98.20oF, the standard deviation is 0.62oF, and the minimum is 96.5oF.a. What is the difference between the minimum and the mean?b. How many standard deviations is
Female Pulse Rates For the pulse rates of females listed in Data Set 1 “Body Data” in Appendix B, the mean is 74.0 BPM, the standard deviation is 12.5 BPM, and the minimum is 36 BPM.a. What is the difference between the minimum and the mean?b. How many standard deviations is that [the
Female Pulse Rates For the pulse rates of females listed in Data Set 1 “Body Data” in Appendix B, the mean is 74.0 BPM, the standard deviation is 12.5 BPM, and the maximum is 104 BPM.a. What is the difference between the maximum and the mean?b. How many standard deviations is that [the
z Scores If your score on your next statistics test is converted to a z score, which of these z scores would you prefer: -2.00,-1.00, 0, 1.00, 2.00? Why?
z Scores LeBron James, one of the most successful basketball players of all time, has a height of 6 feet 8 inches, or 203 cm. Based on statistics from Data Set 1 “Body Data” in Appendix B, his height converts to the z score of 4.07. How many standard deviations is his height above the mean?
Foot Lengths Based on Data Set 7 “Foot and Height” in Appendix B, adult males have foot lengths with a mean of 27.32 cm and a standard deviation of 1.29 cm. Is the adult male foot length of 30 cm significantly low or significantly high? Explain.
Pulse Rates of Males Based on Data Set 1 “Body Data” in Appendix B, males have pulse rates with a mean of 69.6 beats per minute and a standard deviation of 11.3 beats per minute. Is a male pulse rate of 50 beats per minute significantly low or significantly high? (All of these pulse rates are
Pulse Rates of Females Based on Data Set 1 “Body Data” in Appendix B, females have pulse rates with a mean of 74.0 beats per minute and a standard deviation of 12.5 beats per minute. Is a female pulse rate of 44 beats per minute significantly low or significantly high?(All of these pulse rates
Births Exercise 24 Estimating Standard Deviation with the Range Rule of Thumb. In Exercises 25–28, refer to the data in the indicated exercise. After finding the range of the data, use the range rule of thumb to estimate the value of the standard deviation. Compare the result to the standard
Body Temperatures Exercise 23 Estimating Standard Deviation with the Range Rule of Thumb. In Exercises 25–28, refer to the data in the indicated exercise. After finding the range of the data, use the range rule of thumb to estimate the value of the standard deviation. Compare the result to the
LDL Exercise 22 Estimating Standard Deviation with the Range Rule of Thumb. In Exercises 25–28, refer to the data in the indicated exercise. After finding the range of the data, use the range rule of thumb to estimate the value of the standard deviation. Compare the result to the standard
HDL Exercise 21 Estimating Standard Deviation with the Range Rule of Thumb. In Exercises 25–28, refer to the data in the indicated exercise. After finding the range of the data, use the range rule of thumb to estimate the value of the standard deviation. Compare the result to the standard
Births Use the birth weights (grams) of the 400 babies listed in Data Set 3 “Births” in Appendix B. Examine the list of birth weights to make an observation about those numbers.How does that observation affect the way that the results should be rounded?
LDL Repeat the preceding exercise using the LDL measurements (mg>dL).
HDL Use the HDL cholesterol measurements (mg>dL) from the 300 subjects included in Data Set 1 “Body Data” in Appendix B. Identify the highest value. Does it appear to be an outlier?Do the measures of variation change much when that highest value is deleted?
Queues A Providence Hospital experiment involves two different waiting line configurations for patients arriving for admission. The waiting times (in seconds) are recorded with a single line configuration that feeds four stations and another configuration with individual lines at the four
White ,Red Blood Counts Listed below are white blood cell counts (1000 cells>mL)and red blood cell counts (million cells>mL) from different subjects (from Data Set 1 “Body Data” in Appendix B). The values are matched so that each of the 12 subjects has a white blood cell count and a red blood
Blood Pressure A sample of blood pressure measurements is taken from Data Set 1 “Body Data” in Appendix B, and those values (mm Hg) are listed below. The values are matched so that 10 subjects each have systolic and diastolic measurements.Subject: 1 2 3 4 5 6 7 8 9 10 Systolic: 118 128 158 96
California Smokers In the California Health Interview Survey, randomly selected adults are interviewed. One of the questions asks how many cigarettes are smoked per day, and results are listed below for 50 randomly selected respondents. How well do the results reflect the smoking behavior of
Firefighter Fatalities Listed below are the numbers of heroic firefighters who lost their lives in the United States each year while fighting forest fires. The numbers are listed in order by year, starting with the year 2000. What important feature of the data is not revealed by any of the measures
Cell Phone Radiation Listed below are the measured radiation absorption rates (in W>kg)corresponding to these cell phones: iPhone 5S, BlackBerry Z30, Sanyo Vero, Optimus V, Droid Razr, Nokia N97, Samsung Vibrant, Sony Z750a, Kyocera Kona, LG G2, and Virgin Mobile Supreme. The data are from the
TV Prices A physician plans to buy a television for her large waiting room. Listed below are selling prices (in dollars) of TVs that are 60 inches or larger and rated as a “best buy” by Consumer Reports magazine. Are the resulting statistics representative of the population of all TVs that are
Peas in a Pod Biologists conducted experiments to determine whether a deficiency of carbon dioxide in the soil affects the phenotypes of peas. Listed below are the phenotype codes, where 1 = smooth @ yellow, 2 = smooth @ green, 3 = wrinkled @yellow, and 4 = wrinkled @ green. Do the results make
Football Player Weights Listed below are the weights (lb) of 11 players randomly selected from the roster of the Seattle Seahawks when they won Super Bowl XLVIII (the same players from the preceding exercise). Are the results likely to be representative of all NFL players?189 254 235 225 190 305
Variance The 20 subjects used in Data Set 9 “IQ and Brain Size” in Appendix B have weights with a standard deviation of 20.0414 kg. What is the variance of their weights? Include the appropriate units with the result.
Range Rule of Thumb for Interpreting s The 20 brain volumes (cm3) from Data Set 9“IQ and Brain Size” in Appendix B have a mean of 1126.0 cm3 and a standard deviation of 124.9 cm3. Use the range rule of thumb to identify the limits separating values that are significantly low or significantly
Range Rule of Thumb for Estimating s The 20 brain volumes (cm3) from Data Set 9“IQ and Brain Size” in Appendix B vary from a low of 963 cm3 to a high of 1439 cm3. Use the range rule of thumb to estimate the standard deviation s and compare the result to the exact standard deviation of 124.9 cm3.
Weighted Mean A student of one of the authors earned grades of 63, 91, 88, 84, and 79 on her five regular statistics tests. She earned a grade of 86 on the final exam and 90 on her class projects. Her combined homework grade was 70. The five regular tests count for 60%of the final grade, the final
Weighted Mean A student of one of the authors earned grades of A, C, B, A, and D.Those courses had these corresponding numbers of credit hours: 3, 3, 3, 4, and 1. The grading system assigns quality points to letter grades as follows: A = 4; B = 3; C = 2; D = 1;F = 0. Compute the grade-point average
Body Temperatures Refer to Data Set 2 “Body Temperatures” in Appendix B and use the body temperatures for 12:00 AM on day 2. Do the results support or contradict the common belief that the mean body temperature is 98.6oF?
LDL Repeat the preceding exercise using the low-density lipoprotein (LDL) measurements(mg>dL).
HDL Use the high-density lipoprotein (HDL) cholesterol measurements (mg>dL) from the 300 subjects included in Data Set 1 “Body Data” in Appendix B. Identify the highest value.Does it appear to be an outlier? Do the mean and median change much when that highest value is deleted?
Queues A Providence Hospital experiment involves two different waiting line configurations for patients arriving for admission. The waiting times (in seconds) are recorded with a single line configuration that feeds four stations and another configuration with individual lines at the four stations.
White Blood Counts Listed below are white blood cell counts (1000 cells>mL) from males and females (from Data Set 1 “Body Data” in Appendix B). Do they appear to be different?Female: 8.7 6.9 8.1 8.0 6.9 8.1 6.4 6.3 10.9 4.8 5.9 7.2 Male: 4.9 7.5 6.1 5.7 4.1 5.6 8.3 5.1 9.5 6.1 5.7 5.4
White>Red Blood Counts Listed below are white blood cell counts (1000 cells>mL)and red blood cell counts (million cells>mL) from different subjects (from Data Set 1 “Body Data” in Appendix B). The values are matched so that each of the 12 subjects has a white blood cell count and a red blood
Blood Pressure A sample of blood pressure measurements is taken from Data Set 1 “Body Data” in Appendix B, and those values (mm Hg) are listed below. The values are matched so that 10 subjects each have systolic and diastolic measurements. (Systolic is a measure of the force of blood being
California Smokers In the California Health Interview Survey, randomly selected adults are interviewed. One of the questions asks how many cigarettes are smoked per day, and results are listed below for 50 randomly selected respondents. How well do the results reflect the smoking behavior of
Medical School Tuition Listed below in dollars are the annual costs of tuition at the 10 most expensive private medical schools in the United States for a recent year (based on data from U.S. News & World Report). What does this “top 10” list tell us about those costs for the population of all
Foot Lengths Listed below are foot lengths in inches of randomly selected Army women measured in the 1988 Anthropometric Survey (ANSUR). Are the statistics representative of the current population of all Army women?10.4 9.3 9.1 9.3 10.0 9.4 8.6 9.8 9.9 9.1 9.1
Firefighter Fatalities Listed below are the numbers of heroic firefighters who lost their lives in the United States each year while fighting forest fires. The numbers are listed in order by year, starting with the year 2000. What important feature of the data is not revealed by any of the measures
Caffeine in Soft Drinks Listed below are measured amounts of caffeine (mg per 12 oz of drink) obtained in one can from each of 20 brands (7-UP, A&W Root Beer, Cherry Coke,. . . , Tab). Are the statistics representative of the population of all cans of the same 20 brands consumed by Americans?0 0 34
TV Prices A physician plans to buy a television for her large waiting room. Listed below are selling prices in dollars of TVs that are 60 inches or larger and rated as a “best buy” by Consumer Reports magazine. Are the resulting statistics representative of the population of all TVs that are 60
Peas in a Pod Biologists conducted experiments to determine whether a deficiency of carbon dioxide in the soil affects the phenotypes of peas. Listed below are the phenotype codes, where 1 = smooth@yellow, 2 = smooth@green, 3 = wrinkled@yellow, and 4 = wrinkled@green. Can the measures of center be
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