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descriptive statistics
Introductory Statistics For The Life And Biomedical Sciences 1st Edition Julie Vu, David Harrington - Solutions
Consider the standard normal distribution with mean \(\mu=0\) and standard deviation \(\sigma=1\).(a) What is the probability that an outcome \(Z\) is greater than 2.60?(b) What is the probability that \(Z\) is less than 1.35?(c) What is the probability that \(Z\) is between -1.70 and 3.10?(d) What
In triathlons, it is common for racers to be placed into age and gender groups. The finishing times of men ages 30-34 has mean of 4,313 seconds with a standard deviation of 583 seconds. The finishing times of the women ages 25-29 has a mean of 5,261 seconds with a standard deviation of 807 seconds.
The Graduate Record Examination (GRE) is a standardized test commonly taken by graduate school applicants in the United States. The total score is comprised of three components: Quantitative Reasoning, Verbal Reasoning, and Analytical Writing. The first two components are scored from 130 - 170. The
The World Health Organization defines osteoporosis in young adults as a measured bone mineral density 2.5 or more standard deviations below the mean for young adults. Assume that bone mineral density follows a normal distribution in young adults. What percentage of young adults suffer from
A study investigating maternal investment in a frog species found on the Tibetan Plateau reported data on the volume of egg clutches measured across 11 study sites. The distribution is roughly normal, with approximate distribution \(N(882.5,380) \mathrm{mm}^{3}\).(a) What is the probability of
Fasting blood glucose levels for normal non-diabetic individuals are normally distributed in the population, with mean \(\mu=85 \mathrm{mg} / \mathrm{dL}\) and standard deviation \(\sigma=7.5 \mathrm{mg} / \mathrm{dL}\).(a) What is the probability that a randomly chosen member of the population has
Arsenic blood concentration is normally distributed with mean \(\mu=3.2 \mu \mathrm{g} / \mathrm{dl}\) and standard deviation \(\sigma=1.5 \mu \mathrm{g} / \mathrm{d}\). What range of arsenic blood concentration defines the middle \(95 \%\) of this distribution?
In the last decade, the average age of a mother at childbirth is 26.4 years, with standard deviation 5.8 years. The distribution of age at childbirth is approximately normal.(a) What proportion of women who give birth are 21 years of age or older?(b) Giving birth at what age puts a woman in the
Find the standard deviation of the distribution in the following situations.(a) MENSA is an organization whose members have IQs in the top \(2 \%\) of the population. IQs are normally distributed with mean 100, and the minimum IQ score required for admission to MENSA is 132.(b) Cholesterol levels
The final exam scores of 20 introductory statistics students are plotted below. Do these data appear to follow a normal distribution? Explain your reasoning. 60 60 70 80 Scores 90 00 90 90 Sample Quantiles 70- 60 60 -1 Theoretical Quantiles -2
The heights of 25 female college students are plotted below. Do these data appear to follow a normal distribution? Explain your reasoning. 50 55 60 Heights Sample Quantiles 70- 65 60 60 55 65 70 75 -1 Theoretical Quantiles 2
This is a simple exercise in computing probabilities for a Poisson random variable. Suppose that \(X\) is a Poisson random variable with rate parameter \(\lambda=2\). Calculate \(P(X=2)\), \(P(X \leq 2)\), and \(P(X \geq 3)\).
Osteosarcoma is a relatively rare type of bone cancer. It occurs most often in young adults, age 10 - 19; it is diagnosed in approximately 8 per \(1,000,000\) individuals per year in that age group. In New York City (including all five boroughs), the number of young adults in this age range is
Occasionally an airline will lose a bag. Suppose a small airline has found it can reasonably model the number of bags lost each weekday using a Poisson model with a mean of 2.2 bags.(a) What is the probability that the airline will lose no bags next Monday?(b) What is the probability that the
Hemophilia is a sex-linked bleeding disorder that slows the blood clotting process. In severe cases of hemophilia, continued bleeding occurs after minor trauma or even in the absence of injury. Hemophilia affects 1 in 5,000 male births. In the United States, about 400 males are born with hemophilia
The US Centers for Disease Control (CDC) has been monitoring the rate of deaths from opioid overdoses for at least the last 15 years. In 2013, the rate of opioid-related deaths has risen to 6.8 deaths per year per 100,000 non-Hispanic white members. In 2014-2015, the population of Essex County, MA,
Recall from Problem 3.11 that a patient with Type O+ blood can receive either Type O+ or Type O- blood, while a patient with Type O- blood can only receive Type O- blood. According to data collected from blood donors, 0.37 of white, non-Hispanic donors are Type \(\mathrm{O}+\) and 0.08 are Type O-.
Recall from Problem 3.15 that \(30 \%\) of the Drosophila stocks at the BDSC are infected with Wolbachia. Suppose a research assistant randomly samples a stock one at a time until identifying an infected stock.(a) Calculate the probability that an infected stock is found within the first 5 stocks
Cilantro leaves are widely used in many world cuisines. While some people enjoy it, others claim that it has a soapy, pungent aroma. A recent study conducted on participants of European ancestry identified a genetic variant that is associated with soapy-taste detection. In the initial
Recall from Problem 3.53 that in a questionnaire, 1,994 respondents out of 14,604 reported that they thought cilantro tasted like soap. Suppose that a random sample of 15 individuals are selected for further study.(a) What is the mean and variance of the number of people sampled that are
A study to examine oral health of schoolchildren in Belgium found that of the 4,351 children examined, \(44 \%\) were caries free (i.e., free of decay, restorations, and missing teeth). Suppose that children are sampled one by one.(a) What is the probability that at least three caries free children
Suppose \(X\) and \(Y\) have the following joint distribution.(a) Calculate the marginal distributions of \(X\) and \(Y\).(b) Calculate the mean, variance, and standard deviation of \(X\).(c) What are the standardized values of \(X\) ?(d) The mean and standard deviation of \(Y\) are 0 and 1,
Suppose \(X\) and \(Y\) have the following joint distribution.(a) Are \(X\) and \(Y\) independent?(b) Calculate the correlation between \(X\) and \(Y\).(c) Are your answers to parts (a) and (b) consistent? Explain your answer. Y = -1 Y = 1 X = 0 0.25 0.25 X = 1 0.25 0.25
Let \(X\) represent the outcome from a roll of a fair six-sided die. Then, toss a fair coin \(X\) times and let \(Y\) denote the number of tails observed.(a) Consider the joint probability table of \(X\) and \(Y\). How many entries are in the table for the joint distribution of \(X\) and \(Y\) ?
In the health insurance example introduced in Example 3.6, the largest annual expense for the annual employee \((\$ 1,108)\) was caused by 8 visits to a provider for a knee injury requiring physical therapy. The couple has confidence that this or a similar injury will not happen again in the coming
The evolutionary role of variation in bird egg coloration remains mysterious to biologists. One hypothesis suggests that egg color may play a role in sexual selection. For example, perhaps healthier females are able to deposit more blue-green pigment into eggshells instead of using it themselves as
The 2009 holiday retail season, which kicked off on November 27, 2009 (the day after Thanksgiving), had been marked by somewhat lower self-reported consumer spending than was seen during the comparable period in 2008. To get an estimate of consumer spending, 436 randomly sampled American adults
The General Social Survey (GSS) is a sociological survey used to collect data on demographic characteristics and attitudes of residents of the United States. The 2010 General Social Survey asked the question, "For how many days during the past 30 days was your mental health not good?" Based on
In 2010, the General Social Survey collected responses from 1,154 US residents. The survey is conducted face-to-face with an in-person interview of a randomly selected sample of adults. One of the questions on the survey is "After an average workday, about how many hours do you have to relax or
Age at first marriage, Part II. Exercise 4.8 presents the results of a 2006 - 2010 survey showing that the average age of women at first marriage is 23.44. Suppose a social scientist believes that this value has increased in 2012, but she would also be interested if she found a decrease. Below is
Researchers investigating characteristics of gifted children collected data from schools in a large city on a random sample of thirty-six children who were identified as gifted children soon after they reached the age of four. The following histogram shows the distribution of the ages (in months)
The hospital administrator mentioned in Exercise 4.7 randomly selected 64 patients and measured the time (in minutes) between when they checked in to the ER and the time they were first seen by a doctor. The average time is 137.5 minutes and the standard deviation is 39 minutes. She is getting
Suppose an investigator takes a random sample of \(n=50\) birth weights from several teaching hospitals located in an inner-city neighborhood. In her random sample, the sample mean \(\bar{x}\) is 3,150 grams and the standard deviation is 250 grams.(a) Calculate a \(95 \%\) confidence interval for
Exercise 4.16 describes a study on gifted children. In this study, along with variables on the children, the researchers also collected data on the mother's and father's IQ of the 36 randomly sampled gifted children. The histogram below shows the distribution of mother's IQ. Also provided are some
A migraine is a particularly painful type of headache, which patients sometimes wish to treat with acupuncture. To determine whether acupuncture relieves migraine pain, researchers conducted a randomized controlled study where 89 females diagnosed with migraine headaches were randomly assigned to
The Buteyko method is a shallow breathing technique developed by Konstantin Buteyko, a Russian doctor, in 1952. Anecdotal evidence suggests that the Buteyko method can reduce asthma symptoms and improve quality of life. In a scientific study to determine the effectiveness of this method,
Researchers hypothesized that a particular taste receptor in hummingbirds, T1R1-T1R3, played a primary role in dictating taste behavior; specifically, in determining which compounds hummingbirds detect as sweet. In a series of field tests, hummingbirds were presented simultaneously with two filled
The evolutionary significance of variation in egg coloration among birds is not fully understood. One hypothesis suggests that egg coloration may be an indication of female quality, with healthier females being capable of depositing blue-green pigment into eggshells instead of using it for
A study was conducted to assess whether the abundance of particular bacterial species in the gastrointestinal system is associated with the development of colon cancer.The following data matrix shows a subset of the data collected in the study. Cancer stage is coded 1-4, with larger values
Echinacea has been widely used as an herbal remedy for the common cold, but previous studies evaluating its efficacy as a remedy have produced conflicting results. In a new study, researchers randomly assigned 437 volunteers to receive either a placebo or echinacea treatment before being infected
Exercise 1.4 introduces a study on using the Buteyko shallow breathing technique to reduce asthma symptoms and improve quality of life. As part of this study 600 asthma patients aged 18-69 who relied on medication for asthma treatment were recruited and randomly assigned to two groups: one
In order to assess the effectiveness of taking large doses of vitamin C in reducing the duration of the common cold, researchers recruited 400 healthy volunteers from staff and students at a university. A quarter of the patients were randomly assigned a placebo, and the rest were randomly allocated
Environmental factors early in life can have long-lasting effects on an organism.In one study, researchers examined whether dietary supplementation with vitamins C and E influences body mass and corticosterone level in yellow-legged gull chicks. Chicks were randomly assigned to either the non
The following scatterplot was created as part of a study evaluating the relationship between estimated life expectancy at birth (as of 2014) and percentage of internet users (as of 2009) in 208 countries for which such data were available.(a) Describe the relationship between life expectancy and
An observational study published last year in The American Journal of Preventive Medicine investigated the effects of an increased alcohol sales tax in Maryland on the rates of gonorrhea and chlamydia. After a tax increase from 6% to 9% in 2011, the statewide gonorrhea rate declined by 24%, the
Since states with larger numbers of elderly residents would naturally have more nursing home residents, the number of nursing home residents in a state is often adjusted for the number of people 65 years of age or order (65+). That adjustment is usually given as the number of nursing home residents
Suppose that an anonymous questionnaire is given to patients at a dentist’s office once they arrive for an appointment. One of the questions asks "How often do you floss?", and four answer options are provided:a) at least twice a day, b) at least once a day, c) a few times a week, and d) a few
Data are available on the number of children born to women aged 15-19 from 189 countries in the world for the years 1997, 2000, 2002, 2005, and 2006. The data are defined using a scaling similar to that used for the nursing home data in Exercise 1.30. The values for the annual adolescent fertility
Researchers collected data from an observational study to investigate the association between smoking status and the presence of aortic stenosis, a narrowing of the aorta that impedes blood flow to the body.(a) What percentage of the 215 participants were both smokers and had aortic stenosis? This
Trait anger is defined as a relatively stable personality trait that is manifested in the frequency, intensity, and duration of feelings associated with anger. People with high trait anger have rage and fury more often, more intensely, and with long-laster episodes than people with low trait anger.
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