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Statistics For The Life Sciences 5th Edition Myra Samuels, Jeffrey Witmer, Andrew Schaffner - Solutions

Agronomists measured the yield of a variety of hybrid corn in 16 locations in Illinois. The data, in bushels per acre, were(a) Construct a dotplot of the data. (b) Describe the shape of the distribution.
Trypanosomes are parasites that cause disease in humans and animals. In an early study of trypanosome morphology, researchers measured the lengths of 500 individual trypanosomes taken from the blood of a rat. The results are summarized in the accompanying frequency distribution.(a) Construct a
As part of a classic experiment on mutations, 10 aliquots of identical size were taken from the same culture of the bacterium E. coli. For each aliquot, the number of bacteria resistant to a certain virus was determined. The results were as follows:(a) Construct a frequency distribution of these
The accompanying table gives the litter size (number of piglets surviving to 21 days) for each of 36 sows (as in Example 2.2.4). Determine the median litter size.
Here is a histogram.(a) Estimate the median of the distribution. (b) Estimate the mean of the distribution.
A researcher applied the carcinogenic (cancer-causing) compound benzo (a) pyrene to the skin of five mice, and measured the concentration in the liver tissue after 48 hours. The results (nmol/gm) were as follows:Determine the mean and the median.
Consider the data from Exercise 2.3.7. Are the calculated mean and median consistent with the claim that, in general, steers gain 3.5 lb/day? Are they consistent with a claim of 4.0 lb/day?
Here are the data from Exercise 2.3.10 on the number of virus-resistant bacteria in each of 10 aliquots:(a) Determine the median and the quartiles.(b) Determine the interquartile range.(c) I low large would an observation in this data set have to be in order to be an outlier?
Here are the 18 measurements of MAO activity reported in Exercise 2.2.2:(a) Determine the median and the quartiles. (b) Determine the interquartile range. (c) How large would an observation in this data set have to be in order to be an outlier? (d) Construct a boxplot of the data.
In a study of milk production in sheep (for use in making cheese), a researcher measured the 3-month milk yield for each of 11 ewes. The yields (liters) were as follows:(a) Determine the median and the quartiles. (b) Determine the interquartile range. (c) Construct a boxplot of the data.
For each of the following histograms, use the histogram to estimate the median and the quartiles; then construct a boxplot for the distribution.(a)(b)
The following boxplot shows the five-number summary for a data set. For these data the minimum is 35, Q1 is 42, the median is 49, Q3, is 56, and the maximum is 65. Is it possible that no observation in the data set equals 42? Explain your answer.
Statistics software can be used to find the five-number summary of a data set. Here is an example of MINITAB's descriptive statistics summary for a variable stored in column 1 (CI) of MINITAB's worksheet.(a) Use the MINITAB output to calculate the inter-quartile range. (b) Are there any outliers in
Consider the data from Exercise 2.4.7. Use the five-number summary that is given to create a boxplot of the data.Exercise 2.4.7.Statistics software can be used to find the five-number summary of a data set. Here is an example of MINITAB's descriptive statistics summary for a variable stored in
The two claws of the lobster (Homarus americanus) are identical in the juvenile stages. By adulthood, however, the two claws normally have differentiated into a stout claw called a "crusher" and a slender claw called a "cutter." In a study of the differentiation process, 26 juvenile animals were
Does the length (mm) of the golden mantled ground squirrel (Spermophilus lateralis) differ by latitude in California? A graduate student captured squirrels at four locations across California. Listed from south to north the locations are Hemet, Big Bear, Susanville, and Loop Hill.(a) Create
The rowan (Sorbus aucuparia) is a tree that grows in a wide range of altitudes. To study how the tree adapts to its varying habitats, researchers collected twigs with attached buds from 12 trees growing at various altitudes in North Angus, Scotland. The buds were brought back to the laboratory and
A group of college students were asked how many hours per week they exercise.34The answers given by 12 men were as follows:The answers given by 13 women were as follows: (a) Construct parallel boxplots of the male and female distributions. (b) Describe the two boxplots, including how they compare
Calculate the SD of each of the following fictitious samples: (a) 16,13,18,13 (b) 38, 30, 34, 38, 35 (c) 1, - 1, 5, - 1 (d) 4, 6, -1, 4, 2
Compare the results of Exercise 2.6.9 with the predictions of the empirical rule.
Listed in increasing order are the serum creatine phosphokinase (CK) levels (U/l) of 36 healthy men (these arc the data of Example 2.2.6):The sample mean CK level is 98.3 U/l and the SD is 40.4 U/l. What percentage of the observations are within(a) 1 SD of the mean?(b) 2 SDs of the mean?(c) 3 SDs
Compare the results of Exercise 2.6.11 with the predictions of the empirical rule.
As part of the Berkeley Guidance Study the heights (in cm) and weights (in kg) of 13 girls were measured at age 2 and again at age 9. Of course, the average height and weight were much greater at age 9 than at age 2. Likewise, the SDs of height and of weight were much greater at age 9 than they
Here is a histogram. Estimate the mean and the SD of the distribution.
Here is a histogram. Estimate the mean and the SD of the distribution.
For which sample (i or ii) would you expect the SD of heights to be larger? Or, would they be about the same? (a) (i) A sample of 10 women ages 18-24, or (ii) a sample of 100 women ages 18-24. (b) (i) A sample of 20 male college basketball players, or (ii) a sample of 20 college-age men. (c) (i) A
Calculate the SD of each of the following fictitious samples: (a) 8, 6, 9, 4, 8 (b) 4, 7, 5, 4 (c) 9, 2, 6, 7, 6
(a) Invent a sample of size 5 for which the deviations (y, - y) are -3, - 1, 0, 2, 2. (b) Compute the SD of your sample. (c) Should everyone get the same answer for part (b)? Why or why not?
Ten patients with high blood pressure participated in a study to evaluate the effectiveness of the drug Timolol in reducing their blood pressure. The accompanying table shows systolic blood pressure measurements taken before and after 2 weeks of treatment with Timolol. Calculate the mean and SD of
Dopamine is a chemical that plays a role in the transmission of signals in the brain. A pharmacologist measured the amount of dopamine in the brain of each of seven rats. The dopamine levels (nmoles/g) were as follows:(a) Calculate the mean and SD.(b) Determine the median and the interquartile
In a study of the lizard Sceloporus occidentals biologists measured the distance (m) run in 2 minutes for each of 15 animals. The results (listed in increasing order) were as follows:(a) Determine the quartiles and the interquartile range. (b) Determine the range.
Refer to the running-distance data of Exercise 2.6.8. The sample mean is 32.23 m and the SD is 8.07 m. What percentage of the observations are within(a) 1 SD of the mean?(b) 2 SDs of the mean?Exercise 2.6.8In a study of the lizard Sceloporus occidentals biologists measured the distance (m) run in 2
2.7.2 The mean and SD of a set of 47 body temperature measurements were as follows: = 36.497°C s = 0.172°C If the 47 measurements were converted to °F, (a) What would be the new mean and SD? (b) What would be the new coefficient of variation?
A researcher measured the average daily gains (in kg/day) of 20 beef cattle; typical values wereThe mean of the data was 1.461 and the SD was 0.178. (a) Express the mean and SD in lb/day. (b) Calculate the coefficient of variation when the data are expressed (i) in kg/day; (ii) in lb/day.
The following histogram shows the distribution for a sample of data:
A sample of four students had the following heights (in cm): 180. 182. 179. 176. Suppose a fifth student were added to the group. How tall would that student have to be to make the mean height of the group equal 181?
Calculate the SD of each of the following fictitious samples: (a) 11, 8, 4, 10, 7 (b) 23, 29, 24, 21, 23 (c) 6, 0, - 3, 2, 5
To study the spatial distribution of Japanese beetle larvae in the soil, researchers divided a 12- Ã— 12-foot section of a cornfield into 144 one-foot squares. They counted the number of larvae Y in each square, with the results shown in the following table.(a) The mean and SD of Y are = 2.23
One measure of physical fitness is maximal oxygen uptake, which is the maximum rate at which a person can consume oxygen. A treadmill test was used to determine the maximal oxygen uptake of nine college women before and after participation in a 10-week program of vigorous exercise. The accompanying
A veterinary anatomist investigated the spatial arrangement of the nerve cells in the intestine of a pony. He removed a block of tissue from the intestinal wall, cut the block into many equal sections, and counted the number of nerve cells in each of 23 randomly selected sections. The counts were
A geneticist counted the number of bristles on a certain region of the abdomen of the fruitfly Drosophila melanogaster. The results for 119 individuals were as shown in the table.(a) Find the median number of bristles.(b) Find the first and third quartiles of the sample.(c) Make a boxplot of the
The carbon monoxide in cigarettes is thought to be hazardous to the fetus of a pregnant woman who smokes. In a study of this hypothesis, blood was drawn from pregnant women before and after smoking a cigarette. Measurements were made of the percent of blood hemoglobin bound to carbon monoxide as
A medical researcher in India obtained blood specimens from 31 young children, all of whom were infected with malaria. The following data, listed in increasing order, are the numbers of malarial parasites found in 1 ml of blood from each child.(a) Construct a frequency distribution of the data,
Rainfall, measured in inches, for the month of June in Cleveland, Ohio, was recorded for each of 41 years 63 The values had a minimum of 1.2, an average of 3.6, and an SD of 1.6. Which of the following is a rough histogram for the data? How do you know?
The following histograms (a), (b), and (c) show three distributions.The accompanying computer output shows the mean, median, and SD of the three distributions, plus the mean, median, and SD for a fourth distribution. Match the histograms with the statistics. Explain your reasoning. (One set of
A botanist grew 15 pepper plants on the same greenhouse bench. After 21 days, she measured the total stem length (cm) of each plant, and obtained the following values:(a) Construct a dotplot for these data, and mark the positions of the quartiles. (b) Calculate the interquartile range. (c) Are
The following boxplots show morality rates (death within one year per 100 patients) for heart transplant patients at various hospitals. The low-volume hospitals are those that perform between 5 and 9 transplants per year. The high-volume hospitals perform 10 or more transplants per year. Describe
Physicians measured the concentration of calcium (nM) in blood samples from 38 healthy persons. The data are listed as follows.Calculate appropriate measures of the center and spread of the distribution. Describe the shape of the distribution and any unusual features in the data.
The following boxplot shows the same data that are shown in one of the three histograms. Which histogram goes with the boxplot? Explain your answer.
In a behavioral study of the fruit fly Drosophila melanogaster, a biologist measured, for individual flies, the total time spent preening during a 6-minute observation period. The following are the preening times (sec) for 20 flies:(a) Determine the median and the quartiles. (b) Determine the
To calibrate a standard curve for assaying protein concentrations, a plant pathologist used a spectrophotometer to measure the absorbance of light (wavelength 500 nm) by a protein solution. The results of 27 replicate assays of a standard solution containing 60 µg protein per ml water were as
Refer to the absorbance data of Exercise 2.S.4. (a) Determine the median, the quartiles, and the interquartile range. (b) How large must an observation be to be an outlier? Exercise 2.S.4.
Twenty patients with severe epilepsy were observed for 8 weeks. The following are the numbers of major seizures suffered by each patient during the observation period:(a) Determine the median number of seizures. (b) Determine the mean number of seizures. (c) Construct a histogram of the data. Mark
In a certain population of the freshwater sculpin, Cottus rotheus, the distribution of the number of tail vertebrae is as shown in the table.Find the probability that the number of tail vertebrae in a fish randomly chosen from the population (a) Equals 21. (b) Is less than or equal to 22. (c) Is
The following table shows the distribution of ages of Americans.Age distribution in reference populationFind the probability that the age of a randomly chosen American (a) Is less than 20. (b) Is between 20 and 49. (c) Is greater than 49. (d) Is greater than 29.
In a certain college, 55% of the students are women. Suppose we take a sample of two students. Use a probability tree to find the probability (a) That both chosen students are women. (b) That at least one of the two students is a woman.
If a woman takes an early pregnancy test, she will either test positive, meaning that the test says she is pregnant, or test negative, meaning that the test says she is not pregnant. Suppose that if a woman really is pregnant, there is a 98% chance that she will test positive. Also, suppose that if
Suppose that a medical test has a 92% chance of detecting a disease if the person has it (i.e., 92% sensitivity) and a 94% chance of correctly indicating that the disease is absent if the person really does not have the disease (i.e., 94% specificity). Suppose 10% of the population has the
In a study of the relationship between health risk and income, a large group of people living in Massachusetts were asked a series of questions. Some of the results are shown in the following table.(a) What is the probability that someone in this study smokes? (b) What is the conditional
Consider the data table reported in Exercise 3.3.1. (a) What is the probability that someone in this study is from the low income group and smokes? (b) What is the probability that someone in this study is not from the low income group? (c) What is the probability that someone in this study is from
The following data table is taken from the study reported in Exercise 3.3.1. Here "stressed" means that the pei son reported that most days are extremely stressful or quite stressful; "not stressed" means that the person reported that most days are a bit stressful, not very stressful, or not at all
Consider the data table reported in Exercise 3.3.3. (a) What is the probability that someone in this study has low income? (b) What is the probability that someone in this study either is stressed or has low income (or both)?
Suppose that in a certain population of married couples, 30% of the husbands smoke, 20% of the wives smoke, and in 8% of the couples both the husband and the wife smoke. Is the smoking status (smoker or non-smoker) of the husband independent of that of the wife? Why or why not?
Consider the density curve shown in Figure 3.4.5, which represents the distribution of diameters (measured 4.5 feet above the ground) in a population of 30-year-old Douglas fir trees. Areas under the curve are shown in the figure. What percentage of the trees have diameters (a) Between 4 inches and
Consider the diameter of a Douglas fir tree drawn at random from the population that is represented by the density curve shown in Figure 3.4.5. Find (a) Pr{diameter < 10} (b) Pr{diameter > 4) (c) Pr{2 < diameter < 8}
In a certain population of the parasite Trypanosoma, the lengths of individuals are distributed as indicated by the density curve shown here. Areas under the curve are shown in the figure.Consider the length of an individual trypanosome chosen at random from the population. Find (a) Pr{20 (b)
Consider the distribution of Trypanosoma lengths shown by the density curve in Exercise 3.4.3. Consider the length of an individual trypanosome chosen at random from the population. Find (a) Pr{length < 25} (b) Pr{length > 15} (c) Pr{15 < length < 30}
Consider the distribution of Trypanosoma lengths shown by the density curve in Exercise 3.4.3. Suppose we take a sample of two trypanosomes. What is the probability that (a) Both trypanosomes will be shorter than 20 µ, m? (b) The first trypanosome will be shorter than 20 µ, m and the second
In a certain population of the European starling, there are 5,000 nests with young. The distribution of brood size (number of young in a nest) is given in the accompanying table.Suppose one of the 5,000 broods is to be chosen at random, and let Y be the size of the chosen brood. Find (a) Pr{Y =
Calculate the standard deviation, ÏƒY, of the random variable Y from Exercise 3.5.9.Exercise 3.5.9A group of college students were surveyed to learn how many times they had visited a dentist in the previous year. The probability distribution for Y, the number of visits, is given by the
In the starling population of Exercise 3.5.1, there are 22,435 young in all the broods taken together. (There are 90 young from broods of size 1, there are 460 from broods of size 2, etc.) Suppose one of the young is to be chosen at random, and let Y' be the size of the chosen individual's
Calculate the mean, µY, of the random variable Y from Exercise 3.5.1.Exercise 3.5.1In a certain population of the European starling, there are 5,000 nests with young. The distribution of brood size (number of young in a nest) is given in the accompanying table.
Calculate the standard deviation, ÏƒY, of the random variable Y from Exercise 3.5.4.Exercise 3.5.4Consider a population of the fruit-fly Drosophila melanogaster in which 30% of the individuals are black because of a mutation, while 70% of the individuals have the normal gray body color.
The prevalence of mild myopia (nearsightedness) in adults over age 40 is 25% in the U.S. Suppose four adults over age 40 are chosen at random from the population; let Y denote the number with myopia out of the four. Then the probability distribution for Y is given by the following table:(a) Find
Calculate the mean, µY, of the random variable Y from Exercise 3.5.7.Exercise 3.5.7The prevalence of mild myopia (nearsightedness) in adults over age 40 is 25% in the U.S. Suppose four adults over age 40 are chosen at random from the population; let Y denote the number with myopia out of the
The seeds of the garden pea (Pisuin sativum) are either yellow or green. A certain cross between pea plants produces progeny in the ratio 3 yellow: 1 green. If four randomly chosen progeny of such a cross are examined, what is the probability that (a) Three are yellow and one is green? (b) All four
Neuroblastoma is a rare, serious, but treatable disease. A urine test, the VMA test, has been developed that gives a positive diagnosis in about 70% of cases of neuroblastoma. It has been proposed that this test be used for large-scale screening of children. Assume that 300,000 children are to be
Childhood lead poisoning is a public health concern in the United States. In a certain population, 1 child in 8 has a high blood lead level (defined as 30 µ,g/dl or more). In a randomly chosen group of 16 children from the population, what is the probability that (a) None has high blood lead? (b)
In Australia, 16% of the adult population is near-sighted. If three Australians are chosen at random, what is the probability that (a) Two are nearsighted and one is not? (b) Exactly one is nearsighted? (c) At most one is nearsighted? (d) None of them are nearsighted?
In the United States, 44% of the population has type A blood. Consider taking a sample of size 4. Let Y denote the number of persons in the sample with type A blood. Find (a) Pr{Y = 0}. (b) Pr{Y = 1}. (c) Pr{Y = 2}. (d) Pr{0 ≤ Y ≤ 2). (e) Pr{0 ≤ Y ≤ 2}.
A certain drug treatment cures 90% of cases of hookworm in children. Suppose that 20 children suffering from hookworm are to be treated, and that the children can be regarded as a random sample from the population. Find the probability that (a) All 20 will be cured. (b) All but 1 will be cured. (c)
The shell of the land snail Limocolaria martensiana has two possible color forms: streaked and pallid. In a certain population of these snails, 60% of the individuals have streaked shells. Suppose that a random sample of 10 snails is to be chosen from this population. Find the probability that the
Consider taking a sample of size 10 from the snail population in Exercise 3.6.5.(a) What is the mean number of streaked-shelled snails?(b) What is the standard deviation of the number of streaked-shelled snails?Exercise 3.6.5The shell of the land snail Limocolaria martensiana has two possible color
In Europe, 8% of men are colorblind. Consider taking repeated samples of 20 European men.(a) What is the mean number of colorblind men?(b) What is the standard deviation of the number of colorblind men?
The sex ratio of newborn human infants is about 105 males: 100 females. If four infants are chosen at random, what is the probability that(a) Two are male and two are female?(b) All four are male?(c) All four are the same sex?
Construct a binomial setting (different from any examples presented in this book) and a problem for which the following is the answer: 7C3 (0.8)3(0.2)4.
The accompanying data on families with 6 children are taken from the same study as the families with 12 children in Example 3.7.1. Fit a binomial distribution to the data. (Round the expected frequencies to one decimal place.) Compare with the results in Example 3.7.1. What features do the two data
An important method for studying mutation-causing substances involves killing female mice 17 days after mating and examining their uteri for living and dead embryos. The classical method of analysis of such data assumes that the survival or death of each embryo constitutes an independent binomial
Students in a large botany class conducted an experiment on the germination of seeds of the Saguaro cactus. As part of the experiment, each student planted five seeds in a small cup, kept the cup near a window, and checked every day for germination (sprouting). The class results on the seventh day
Refer to the blood pressure distribution of Exercise 3.S.9. Suppose four men are selected at random from the population. Find the probability that (a) All four have blood pressures higher than 140 mm Hg. (b) Three have blood pressures higher than 140, and one has blood pressure 140 or
In the United States 9% of all people are left-handed.- If we take a random sample of five Americans what is the probability that (a) Exactly four are left-handed? (b) All five are left-handed? (c) At most four are left-handed?
Refer to the distribution of centipedes given in Exercise 3.S.2. Suppose five squares are chosen at random. Find the probability that three of the squares contain centipedes and two do not.Exercise 3.S.2In preparation for an ecological study of centipedes, the floor of a beech woods is divided into
Wavy hair in mice is a recessive genetic trait. If mice with wavy hair are mated with straight-haired (heterozygous) mice, each offspring has probability g of having wavy hair. Consider a large number of such matings, each producing a litter of five offspring. What percentage of the litters will
Refer to Exercise 3.S.6. Suppose now that the dm is to be tested on n patients, and let E represent the even that kidney damage occurs in one or more of the patient The probability Pr{E} is useful in establishing criteria for drug safety. (a) Find Pr{E} for n = 100. (b) How large must n be in order
To study people's ability to deceive lie detectors researchers sometimes use the "guilty knowledge' technique. Certain subjects memorize six common word other subjects memorize no words. Each subject is the tested on a polygraph machine (lie detector), as following the experimenter reads, in random
Suppose a certain population of observations is normally distributed. What percentage of the observations in the population (a) Are within ± 1.5 standard deviations of the mean? (b) Are more than 2.5 standard deviations above the mean? (c) Are more than 3.5 standard deviations away-from (above or
For the serum cholesterol distribution of Exercise 4.3.9, find (a) The 80th percentile (b) The 20th percentile Exercise 4.3.9 The serum cholesterol levels of 12- to 14-year-olds follow a normal distribution with mean 155 mg/dl and standard deviation 27 mg/dl.
When red blood cells are counted using a certain electronic counter, the standard deviation of repeated counts of the same blood specimen is about 0.8% of the true value, and the distribution of repeated counts is approximately normal. For example, this means that if the true value is 5,000,000
The amount of growth, in a 15-day period, for a population of sunflower plants was found to follow a normal distribution with mean 3.18 cm and standard deviation 0.53 cm. What percentage of plants grow (a) 4 cm or more? (b) 3 cm or less? (c) Between 2.5 and 3.5 cm?

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