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the analysis of biological data

The Analysis Of Biological Data 3rd Edition Michael C. Whitlock, Dolph Schluter - Solutions

Smoking is a major risk factor for a number of diseases, including strokes. Smoking is particularly dangerous for people who have already had a stroke. One way to help such people to quit smoking is to make drugs that help stop smoking free to stroke patients. Papadakis et al. (2011) investigated
A “Mediterranean diet” (high in fish, olive oil, red wine, etc.) has been touted as a key to a long life. A study by Trichopoulou et al. (2005) looked at the death rates of people according to whether their diet had a low component, a medium component, or a high component of foods that
The MathWorld web page on hypothesis testing declares that “Hypothesis testing is the use of statistics to determine the probability that a given hypothesis is true” (Weisstein 2018). Is this statement true or false? Explain.
For each of the following scenarios, state a good graphical method to display the data, and state the most appropriate statistical test to address the question.a. Do whales swim past a detector with equal probability over time and independently of each other? The data are measurements of the
Calculation practice: Normal approximation to a binomial test. From 1995 to 2008 in the United States, 531 of the 648 people who were struck by lightning were men. Test whether this proportion is different from the 50% that might be expected by the proportion of men in the population as a whole
A recent cohort study found an increased risk of childhood leukemia in children born to mothers who had previously chosen to use hormonal contraception (Hargreave et al. 2018). The study also noted that use of such contraception was more common for children whose parents were younger, had lower
Assume that ZZ is a number randomly chosen from a standard normal distribution. Use the standard normal table to calculate each of the following probabilities: a. Pr[Z > 1.34] Pr [Z > 1.34]b. Pr[Z < 1.34] Pr [Z < 1.34] c. Pr[Z > 2.15] Pr [Z > 2.15] d. Pr[Z < 1.2] Pr [Z < 1.2] e. Pr[0.52 < Z <
Use the three distributions labeled i, ii, and iii to answer the following questions.a. Which of these distributions is most like the normal distribution? On what basis would you exclude the other two?b. Which distributions would generate an approximately normal distribution of sample means,
It was rumored that Britain’s domestic intelligence service MI5 has an upper limit on the height of its spies, on the assumption that tall people stand out (although MI5 denies it). The rumor said that, to apply to be a spy, you can be no taller than 5 feet 11 inches (180.3 cm) if you are a man,
In the accompanying pairs of graphs of normal distributions, which distribution has the highest mean? Which has the highest standard deviation? Pay careful attention to the changes in scale of the x-axes. x-axes.a.b. Probability density Probability density 0.15 0.10 0.05 0+ T 0 5 10 15 20 25
The babies born in singleton births in the United States have birth weights that are approximately normally distributed with mean 3.296 kg and standard deviation 0.560 kg (Martin et al. 2011).a. What is the probability of a baby being born weighing more than 5 kg?b. What is the probability of a
In the accompanying graph, the red region accounts for 0.67 of the probability density. Estimate the standard deviation of this normal distribution. Probability density 0.04 0.03 0.02 0.01 0 -30 -20 -10 0 Y 10 20 30
Use the two distributions labeled i and ii below to answer the following questions. a. If we drew repeated random samples of individuals from each distribution and calculated the mean for each sample, which distribution would yield a distribution of sample means that most closely followed a
A survey of European mitochondrial DNA variation has found that the most common haplotype (genotype), known as “H,” occurs in 40% of people (Roostalu et al. 2007). If we were to sample 400 individuals from the European population, what is the probability thata. At least 180 are haplotype
The following table lists the means and standard deviations of several different normal distributions. For each, a sample of 10 individuals was taken, as well as a sample of 30 individuals. For each sample, calculate the probability that the mean of the sample was greater than the given value.
Ninety-one out of 220 people working as cast and crew of the movie The Conqueror, which was filmed in 1955 downwind from nuclear bomb tests, ultimately contracted cancer (see Practice Problem 5 in Chapter 7). Based on age alone, though, only a 14% cancer rate was expected. Test the null hypothesis
Assume that ZZ is a number randomly chosen from a standard normal distribution. Use the standard normal table to calculate each of the following probabilities: a. Pr[Z > 0.24]Pr[Z > 0.24]b. Pr[Z < 0.24]Pr[Z < 0.24] c. Pr[Z >2.01]Pr[Z > 2.01] d. Pr[Z < 1.02]Pr[Z < 1.02]e. Pr[0.60 < Z <
The following data are 40 measurements of diameter growth rate of the tropical tree Dipteryx panamensis from a long-term study at La Selva, Costa Rica (Clark and Clark 2012). The data are logtransformed, with the original units in millimeters.a. Make an appropriate graph of the data.b. Examine
The highest recorded temperature during the month of July for a given year in Death Valley, in California, has an approximately normal distribution with a mean of 123.8°F (!) and standard deviation of 3.1°F (Weather Source 2009).a. What is the probability for a given year that the temperature
Draw a distribution that is approximately normal, with mean equal to 10 cm and variance equal to 360. On the same graph, draw the distribution of the means of samples taken from this distribution, if each sample was a random sample of 10 individuals.
In Europe, 53% of flowers of the rewardless orchid, Dactylorhiza sambucina, are yellow, whereas the remaining flowers are purple (Gigord et al. 2001). For this problem, you may use the normal approximation only if it is appropriate to do so.a. If we took a random sample of a single individual from
Recall from Example 10.4 that more women (29.1%) than men (11.1%) are excluded from the astronaut pilot program by the minimum and maximum height restrictions. What value of minimum height for women would exclude the same total proportion of women as men, given that 0.3% of women are too tall?Data
Draw a probability distribution that isn’t normal. Describe the features of your distribution that identify it as non-normal.
Examine the following figure, which displays hypothetical measurements of a sample of individuals from three groups.a. What type of graph is this?b. In which of the groups is the frequency distribution of measurements approximately symmetric?c. Which of the frequency distributions show negative
The following graph shows the maximum age of all individuals whose deaths were recorded in a given year, worldwide (Dong et al. 2016).a. What kind of graph is this?b. Since the data describe a temporal sequence, what other type of plot would be suitable to display them?c. One individual in this
Following is a list of all the named hurricanes in the Atlantic between 2001 and 2010, along with their category on the Saffir-Simpson Hurricane Scale, which categorizes each hurricane by a label from 1 to 5 depending on its power.a. Make a frequency table showing the frequency of hurricanes in
The following graph illustrates an association between two variables. It shows percent changes in the range sizes of different species of native butterflies (red), birds (blue), and plants (black) of Britain over the past two to four decades (data from Thomas et al. 2004). Identify (a) The type
How do the insects that pollinate flowers distinguish individual flowers with nectar from empty flowers? One possibility is that they can detect the slightly higher humidity of the air—produced by evaporation—in flowers that contain nectar. von Arx et al. (2012) tested this idea by manipulating
The gene for the vasopressin receptor V1a is expressed at higher levels in the forebrain of monogamous vole species than in promiscuous vole species. Can expression of this gene influence monogamy? To test this, Lim et al. (2004) experimentally enhanced V1a expression in the forebrain of 11 males
The data in the accompanying table are from an ecological study of the entire rainforest community at El Verde in Puerto Rico (Waide and Reagan 1996). Diet breadth is the number of types of food eaten by an animal species. The number of animal species having each diet breadth is shown in the second
Francis Galton (1894) presented the following data on the flight speeds of 3207 “old” homing pigeons traveling at least 90 miles. a. What type of graph is this?b. Examine the graph and visually determine the approximate value of the mean (to the nearest 100 yards per minute). Explain how you
A study of the endangered saiga antelope (pictured at the beginning of the chapter) recorded the fraction of females in the population that were fecund in each year between 1993 and 2001 (Milner-Gulland et al. 2003). A graph of the data is as follows:a. Assume that you want to describe the
Accurate prediction of the timing of death in patients with a terminal illness is important for their care. The following graph compares the survival times of terminally ill cancer patients with the clinical prediction of their survival times (data from Glare et al. 2003).a. Describe in words what
Convert the following statistics, calculated on samples in English units, to the metric equivalents.(Conversion factors are given as well.)a. Mean: 100 miles (1 km=0.62 miles) b. Standard deviation: 17 miles (1 km=0.62 miles) c. Variance: 289 miles2 (1 km=0.62 miles) d. Coefficient of
Measurements of lifetime reproductive success (LRS) of individual wild animals reveal the disparate contributions they make to the next generation. Jensen et al. (2004) estimated LRS of male and female house sparrows in an island population in Norway. They measured LRS of an individual as the total
As in other vertebrates, individual zebrafish differ from one another along the shy–bold behavioral spectrum. In addition to other differences, bolder individuals tend to be more aggressive, whereas shy individuals tend to be less aggressive. Norton et al. (2011) compared several behaviors
Eunuchs (castrated human males) were often used as servants and guards in harems in Asia and the Middle East. In males of some mammal species, castration increases life span. Do eunuchs also have long lives compared to other men? The accompanying graph shows data on life spans of 81 eunuchs from
As the Arctic warms and winters become shorter, hibernation patterns of arctic mammals are expected to change. Sheriff et al. (2011) investigated emergence dates from hibernation of arctic ground squirrels at sites in the Brooks Range of northern Alaska. The measurements shown in the following
Examine the frequency distribution of gene lengths in the human genome displayed in Figure 4.1-1. Is the population median gene length in the human genome likely to be larger, smaller, or equal to the population mean? Explain.Figure 4.1-1 Population
As a general rule, is the spread of the sampling distribution for the sample mean mainly determined by the magnitude of the mean or by the sample size?
In a poll of 1641 people carried out in Canada in November 2005, 73% of people surveyed agreed with the statement that “you don’t really expect that politicians will keep their election promises once they are in power” (CBC News 2005).a. What is the parameter being estimated?b. What is the
The following data are flash durations, in milliseconds, of a sample of 35 male fireflies of the species Photinus ignitus (Cratsley and Lewis 2003; see Assignment Problem 19 in Chapter 2):a. Estimate the sample mean flash duration. What does this quantity estimate? b. Is the estimate in part (a)
One of the great discoveries of biology is that organisms have a class of genes called “regulatory genes,” whose only job is to regulate the activity of other genes. How many genes does the typical regulatory gene regulate? A study of interaction networks in yeast (S. cerevesiae) came up with
Imagine that a collection of 1600 pea plants from one of Mendel’s experiments had 900 that were tall plants with green pods, 300 that were tall with yellow pods, 300 that were short with green pods, and 100 that were short with yellow pods.a. Are “tall” and “green pods” mutually
Refer to the previous question.a. Draw a frequency distribution of startle durations measured on the first occasion.b. Describe the shape of the frequency distribution: is it skewed or symmetric? If skewed, say whether the skew is positive or negative.Data from previous questionAnimal
Male fireflies of the species Photinus ignitus attract females with pulses of light. Flashes of longer duration seem to attract the most females. During mating, the male transfers a spermatophore to the female. Besides containing sperm, the spermatophore is rich in protein that is distributed by
The accompanying graph depicts a frequency distribution of beak widths of 1017 black-bellied seedcrackers, Pyrenestes ostrinus, a finch from West Africa (Smith 1993).a. What is the mode of the frequency distribution?b. Estimate by eye the fraction of birds whose measurements are in the interval
When its numbers increase following favorable environmental conditions, the desert locust, Schistocerca gregaria, undergoes a dramatic transformation from a solitary, cryptic form into a gregarious form that swarms by the billions. The transition is triggered by mechanical stimulation locusts
The Cambridge Study in Delinquent Development was undertaken in north London (U.K.) to investigate the links between criminal behavior in young men and the socioeconomic factors of their upbringing (Farrington 1994). A cohort of 395 boys was followed for about 20 years, starting at the age of 8 or
Swordfish have a unique “heater organ” that maintains elevated eye and brain temperatures when hunting in deep, cold water. The following graph illustrates the results of a study by Fritsches et al. (2005) that measured how the ability of swordfish retinas to detect rapid motion, measured by
The following graph displays the net number of species listed under the U.S. Endangered Species Act between 1980 and 2002 (U.S. Fish and Wildlife Service 2001):a. What type of graph is this?b. What does the steepness of each line segment indicate?c. Explain what the graph tells us about the
Spot the flaw. Examine the following figure, which displays the frequency distribution of similarity values (the percentage of amino acids that are the same) between equivalent (homologous) proteins in humans and pufferfish of the genus Fugu (data from Aparicio et al. 2002).a. What type of graph
The following data give the photosynthetic capacity of nine individual females of the neotropical tree Ocotea tenera, according to the number of fruits produced in the previous reproductive season (Wheelwright and Logan 2004). The goal of the study was to investigate how reproductive effort in
Examine the accompanying figure, which displays the percentage of adults over 18 with a “body mass index” greater than 25 in different years. Body mass index is a measure of weight relative to height.a. What is the main result displayed in this figure?b. Which of the four principles for
When a courting male of the small Indonesian fish Telmatherina sarasinorum spawns with a female, other males sometimes sneak in and release sperm, too. The result is that not all of the female’s eggs are fertilized by the courting male. Gray et al. (2007) noticed that courting males occasionally
The graph below shows the distribution of age at death for males from Australia.a. What kind of graph is this?b. Describe the shape of the distribution. Is it symmetric or skewed? If it is skewed, describe the type of skew.c. Is this distribution bimodal? Where are the mode or modes?
The following graph was drawn using a very popular spreadsheet program in an attempt to show the frequencies of observations in four hypothetical groups. Before reading further, estimate by eye the frequencies in each of the four groups.a. Identify two features of this graph that cause it to
In Poland, students are required to achieve a score of 21 or higher on the high-school Polish language “maturity exam” to be eligible for university enrollment. The following graph shows the frequency distribution of scores (Freakonomics 2011).a. Examine the graph and identify the most
More than 10% of people carry the parasite Toxoplasma gondii. The following table gives data from Prague on 15- to 29-year-old drivers who had been involved in accidents. The table gives the number of drivers who were infected with Toxoplasma gondii and who were uninfected. These numbers are
The cutoff birth date for school entry in British Columbia, Canada, is December 31. As a result, children born in December tend to be the youngest in their grade, whereas those born in January tend to be the oldest. Morrow et al. (2012) examined how this relative age difference influenced diagnosis
Calculation practice: Law of total probability. The survey in the previous problem was conducted on men as well: 34% say Brussels sprouts are “very repulsive,” 19% say that they are “somewhat repulsive,” 38% are “indifferent,” 8% say they are “somewhat delicious,” and 1% claim they
Calculation practice: General addition rule. Among women voluntarily tested for sexually transmitted diseases in one university, 24% tested positive for human papilloma virus (HPV) only, 2% tested positive for Chlamydia only, and 4% tested positive for both HPV and Chlamydia (Tábora et al. 2005).
The pizza below, ordered from the Venn Pizzeria on Bayes Street, is divided into eight slices:The slices might have pepperoni, mushrooms, olives, and/or anchovies.Imagine that, late at night, you grab a slice of pizza totally at random (i.e., there is a chance that you grabbed any one of the
Calculation practice: General multiplication rule. In the 1980s in Canada, 52% of adult men smoked. It was estimated that male smokers had a lifetime probability of 17.2% of developing lung cancer, whereas a nonsmoker had a 1.3% chance of getting lung cancer during his life (Villeneuve and Mao
In the first hour of a hunting trip, the probability that a pride of Serengeti lions will encounter a Cape buffalo is 0.035. If it encounters a buffalo, the probability that the pride successfully captures it is 0.40 (numbers are from Scheel 1993). What is the probability that the next one-hour
The accompanying bar graph gives the relative frequency of letters in texts from the English language. Such charts are useful for deciphering simple codes.a. If a letter were chosen at random from a book written in normal English, estimate by eye (and a bit of calculation) the probability that it
Cavities in trees are important nesting sites for a wide variety of wildlife, including the white-breasted nuthatch shown on the first page of this chapter.Cavities in trees are much more common in old-growth forests than in recently logged forests. A recent survey in Missouri found that 45 out of
After graduating from your university with a biology degree, you are interviewed for a lucrative job as a snake handler in a circus sideshow. As part of your audition, you must pick up two rattlesnakes from a pit. The pit contains eight snakes, three of which have been defanged and are assumed to
Five different researchers independently take a random sample from the same population and calculate a 95% confidence interval for the same parameter.a. What is the probability that all five researchers have calculated an interval that includes the true value of the parameter?b. What is the
Schrödinger’s cat lives under constant threat of death from the random release of a deadly poison. The probability of release of the poison is 0.01 per day, and the release is independent on successive days.a. What is the probability that the cat will survive 1 day?b. What is the probability
Rapid HIV tests allow for quick diagnosis without expensive laboratory equipment. However, their efficacy has been called into question. In a population of 1517 tested individuals in Uganda, 4 had HIV but tested negative (false negatives), 166 had HIV and tested positive, 129 did not have HIV but
Medical diagnostic tests have “sensitivity” and “specificity.” The sensitivity of a test for a given medical condition is the proportion of all afflicted individuals (i.e., those who have the condition) for whom the test gives a positive result (i.e., the test indicates they indeed have the
Kalani et al. (2008) discovered cells responsive to Wnt proteins in the subventricular zone of developing brains of mouse embryos. These cells included a high fraction of self-renewing stem cells, which suggested that Wnt signaling occurs during brain cell self-renewal. In a particular cell
If you have ever tried to take a family photo, you know that it is very difficult to get a picture in which no one is blinking. It turns out that the probability of an individual blinking during a photo is about 0.04 (Svenson 2006).a. If you take a picture of one person, what is the probability
A normal deck of cards has 52 cards, consisting of 13 each of four suits:spades, hearts, diamonds, and clubs. Hearts and diamonds are red, while spades and clubs are black. Each suit has an ace, nine cards numbered 2 through 10, and three face cards. The face cards are a jack, a queen, and a king.
The human genome is composed of the four DNA nucleotides: A, T, G, and C. Some regions of the human genome are extremely G–C rich (i.e., a high proportion of the DNA nucleotides there are guanine and cytosine). Other regions are relatively A–T rich (i.e., a high proportion of the DNA
In Vancouver, British Columbia, the probability of rain during a winter day is 0.58, for a spring day is 0.38, for a summer day is 0.25, and for a fall day is 0.53. Each of these seasons lasts one quarter of the year.a. What is the probability of rain on a randomly chosen day in
When asked an embarrassing question in a survey—such as whether the respondent has ever shoplifted—individuals may be reluctant to answer truthfully. However, answers might be more truthful if the survey incorporates a random component, such as a coin toss, that prevents the questioner from
The Hox genes are responsible for determining the anterior–posterior identity of body regions (segments) in the developing insect embryo. Different Hox genes are turned on (expressed) in different segments of the body, and in this way they determine which segments become head and which thorax,
Imagine that a long stretch of single-stranded DNA has 30% adenine, 25% thiamine, 15% cytosine, and 30% guanine. (These make up the nucleotides of the DNA.) What is the probability of randomly drawing 10 adenines in a row in a sample of 10 randomly chosen nucleotides?
The flour beetle, Tribolium castaneum, has 10 chromosomes, roughly equal in size, and it also has eight Hox genes (Brown et al. 2002; see Assignment Problem 24). If the eight Hox genes were randomly distributed throughout the genome of the beetle, what is the probability that all eight would land
A seed randomly blows around a complex habitat. It may land on any of three different soil types: a high-quality soil that gives a 0.8 chance of seed survival, a medium-quality soil that gives a 0.3 chance of survival, and a lowquality soil that gives only a 0.1 chance of survival. These three soil
A flycatcher is trying to catch passing bugs. The probability that it catches a bug on any given try is 20%.a. What is the probability that it catches its first bug on its fourth try?b. What is the probability that at least four failures occur before the flycatcher has its first success?
Ignoring leap years, there are 365 days in a year.a. If people are born with equal probability on each of the 365 days, what is the probability that three randomly chosen people have different birthdates?b. If people are born with equal probability on each of the 365 days, what is the probability
The figure at the bottom of the page shows the probability density of colony diameters (in mm) in a hypothetical population of Paenibacillus bacteria. The distribution is continuous, so the probability of sampling a colony within some range of diameter values is given by area under the curve.
During the Manhattan Project, the physicist Enrico Fermi asked Leslie R. Groves, the general in charge, “How do you define a ‘great general’?”General Groves replied, “Any general who wins five battles in a row is great.” He went on to say that only about 3% of generals are great. If
“After taking 10 mammograms, a patient has a 50% chance of having had at least one false alarm.” (A false alarm is a false-positive result.) Given this information (from Elmore et al. 2005), and assuming that false alarms are independent of each other, what is the probability of a false alarm
Refer to the figure accompanying Assignment Problem 31. Consider the case in which two colonies are randomly sampled from the probability distribution shown.a. Are the events “the first diameter is between 4 and 6” and “the second diameter is between 8 and 12” mutually exclusive?
A boy mentions that none of the 21 kids in his third-grade class has had a birthday since school started 56 days previously. Assume that kids in the class are drawn from a population whose birthdays have the same probability on all days of the year. What is the probability that 21 kids in such a
Three variants of the gene encoding the β-globin component of hemoglobin occur in the human population of the Kassena-Nankana district of Ghana, West Africa. The most frequent allele, A, occurs at frequency 0.83.The two other variants, S (“sickle cell”) and C, occur at frequency 0.04 and 0.13,
Refer to Table 5.5-1. It turns out that blood type is controlled by two unlinked genes. One gene determines ABO blood type, and the other determines Rh factor (+ or −). Using the probabilities presented in Table 5.5-1, determine whether the events “individual is blood type O” and “Rh factor
Refer to Assignment Problem 22 in Chapter 2, which gives a data set about the number of criminal convictions for 395 boys in north London. Imagine that you randomly chose one of the 365 boys from this data set.a. What is the probability that this randomly chosen boy had 0 convictions?b. What is
Refer to Assignment Problem 36. If a randomly sampled child has the aa genotype, what is the probability that both its parents were also aa?Data from problem 36Some people are hypersensitive to the smell of asparagus, and can even detect a strong odor in the urine of a person who has recently eaten
The following table was compiled by the U.S. Social Security Administration (2018) and the U.S. Census Bureau (2018). It lists the annual probabilities of death for U.S. residents in their early 20s according to gender (as defined by these U.S. government agencies).a. What is the probability that
Artists often represent abstract concepts with human personifications. Are painters more likely to use a person of the same gender as the grammatical gender of the word describing that concept in their own language? (Unlike English, many languages use grammatical gender: a noun is masculine,
Examine Figure 5.5-2. Using the probability statements on the right-hand side of that figure, what is the probability that exactly one of A or B occurs (i.e., the outcome is just A or just B, but not both)?Figure 5.5-2 + - Pr[A or B] Pr[A] + Pr[B] Pr[A and B] Whitlock & Schluter, The Analysis of
Imagine that you are using a random sample of data to test a null hypothesis. Answer whether the following statement is true or false: A parameter estimate with high sampling error will result in a test with a higher Type I error rate compared to an estimate with low sampling error.
Answer the following questions:a. Define Type II error.b. Define significance level.c. If the significance level of a test is increased, will the probability of making a Type II error increase, decrease, or stay the same? Explain.
Assume that a null hypothesis for a statistical test is true. Say whether each of the following statements is true or false:a. If you reject this H0 with a test, you will be making a Type II error.b. If you fail to reject this H0 with a test, you will be making a Type I error.
Do people have powers of extrasensory perception (ESP)? Some people claim to have such abilities or to know someone who has them. Some people claim that individuals who consistently get the wrong answer must have ESP too. Other people disbelieve such claims. Imagine that you are to set up an

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