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mathematics
statistics

Questions and Answers of Statistics

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
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
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
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)
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
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
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
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
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
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
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
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
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
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
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.
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
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)
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
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
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
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
A biologist made a certain pH measurement in each of 24 frogs; typical values wereShe calculated a mean of 7.373 and a SD of 0.129 for these original pH measurements. Next, she transformed the data
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
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)
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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"
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
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
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
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)
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
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)
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
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
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
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
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
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
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
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
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
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
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
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
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 =
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 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
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
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
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)
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
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
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
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
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)
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
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
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
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
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
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
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
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

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