Questions and Answers of Descriptive Statistics

This question uses data from 500 randomly selected adults in the larger NHANES dataset. Poverty is measured as a ratio of family income to poverty guidelines. Smaller numbers indicate more poverty,
Exercise 7.15 used regression to examine the effect of three interventions on prisoner MMPI scores. The response variable in the regression was trt.effect, the change in MMPI score (pre-intervention
The American Psychological Association defines resilience as "the process of adapting well in the face of adversity, trauma, tragedy, threats, or even significant sources of stress". Studies have
Exercise 7.17 used regression to predict a post-intervention score based on pre-intervention score and a particular intervention. The following table shows a model incorporating interaction between
A study was conducted to evaluate Vitamin D status among schoolchildren in Thailand. Exposure to sunlight allows the body to produce serum $25(\mathrm{OH}) \mathrm{D}$, which is a marker of Vitamin
Exercise 7.1 showed a multiple regression model predicting RFFT score from statin use and age. For this problem, an interaction term is added between statin use and age.(a) Write the model
Antibiotic resistance represents a major public health challenge. Overuse of antibiotics in clinical settings is thought to be a major contributor to increased antibiotic resistance. A study was
Suppose the starting point for model selection for the birth weight data were the full model, with all variables. The table below shows the adjusted $R^{2}$ for the full model as well as the
Suppose the starting point for model selection for the absenteeism data were the full model, with all variables. The table below shows the adjusted $R^{2}$ for the full model as well as the
Exercise 7.5 shows a regression model for predicting the average birth weight of babies based on all variables included in the dataset: length of pregnancy in days (gestation), mother's age in years
Exercise 7.22 introduced a study conducted about antibiotic consumption in China. One aim of the study was to develop a prediction model for predicting monthly average antibiotic consumption based on
Problem 7.15 used a regression model to examine the effect of the interventions on possibly reducing psychopathic deviant $\mathrm{T}$ scores on prisoners. The regression model is shown in the
Exercise 7.18 shows a regression model for the association of BDI score with resilience level.(a) In terms of the variables in the regression model, state the null hypothesis that corresponds to the
In a study of 100 randomly sampled 18 year-old women in an inner city neighborhood, 15 reported that they were taking birth control pills.(a) Can the normal approximation to the binomial distribution
Suppose that the study were repeated in a different inner city neighborhood and that out of 50 randomly sampled 18 -year-old women, 6 reported that they were taking birth control pills. The
A "social experiment" conducted by a TV program questioned what people do when they see a very obviously bruised woman getting picked on by her boyfriend. On two different occasions at the same
In the PREVEND data, researchers measured various features of study participants, including data on statin use and highest level of education attained. A two-way table of education level and statin
Tuberculosis (TB) is an infectious disease caused by the Mycobacterium tuberculosis bacteria. Active TB can be cured by adhering to a treatment regimen of several drugs for 6-9 months. A major
Researchers conducted a study investigating the relationship between caffeinated coffee consumption and risk of depression in women. They collected data on 50,739 women free of depression symptoms at
This problem examines a hypothetical prospective study about an important problem in the developing world: the use of mosquito nets to prevent malaria in children. The nets are typically used to
Most errors in billing insurance providers for health care services involve honest mistakes by patients, physicians, or others involved in the health care system. However, fraud is a serious problem.
Psychologists conducted an experiment to investigate the effect of anxiety on a person's desire to be alone or in the company of others. A group of 30 individuals were randomly assigned into two
Suppose we are interested in investigating the relationship between high salt intake and death from cardiovascular disease (CVD). One possible study design is to identify a group of hig hand low-salt
A professor using an open source introductory statistics book predicts that $60 \%$ of the students will purchase a hard copy of the book, $25 \%$ will print it out from the web, and $15 \%$
An investigator asked for the records of patients diagnosed with diabetes in his practice, then sampled 20 patients with cardiovascular disease (CVD) and 80 patients without CVD. For the sampled
Suppose an investigator has studied the possible association between the use of a weight loss drug and a rare central nervous system (CNS) disorder. He samples from a group of volunteers with and
Asthma is a chronic lung disease characterized as hypersensitivity to a variety of stimuli, such as tobacco smoke, mold, and pollen. The prevalence of asthma has been increasing in recent decades,
In a study examining the association between green tea consumption and esophageal carcinoma, researchers recruited 300 patients with carcinoma and 571 without carcinoma and administered a
Diabetes and hypertension are two of the most common diseases in Western, industrialized nations. In the United States, approximately 9% of the population have diabetes, while about 30% of adults
Urgent care centers are open beyond typical office hours and provide a broader range of services than that of many primary care offices. A study conducted to collect information about urgent care
The ABO blood group system consists of four different blood groups, which describe whether an individual’s red blood cells carry the A antigen, B antigen, both, or neither. The ABO gene has three
Seat belt use is the most effective way to save lives and reduce injuries in motor vehicle crashes. In a 2014 survey, respondents were asked, "How often do you use seat belts when you drive or ride
Swaziland has the highest HIV prevalence in the world: 25.9% of this country’s population is infected with HIV. The ELISA test is one of the first and most accurate tests for HIV. For those who
Assortative mating is a nonrandom mating pattern where individuals with similar genotypes and/or phenotypes mate with one another more frequently than what would be expected under a random mating
A 2013 analysis conducted by the Pew Research Center found that 60% of survey respondents agree with the statement "humans and other living things have evolved over time" while 33% say that "humans
The prevalence of cystic fibrosis in the United States is approximately 1 in 3,500 births. Various screening strategies for CF exist. One strategy uses dried blood samples to check the levels of
Mumps is a highly contagious viral infection that most often occurs in children, but can affect adults, particularly if they are living in shared living spaces such as college dormitories. It is most
About 30% of human twins are identical, and the rest are fraternal. Identical twins are necessarily the same sex – half are males and the other half are females. One-quarter of fraternal twins are
A psychologist conducts a study on intelligence in which participants are asked to take an IQ test consisting of n questions, each with m choices.(a) One thing the psychologist must be careful about
The strongest risk factor for breast cancer is age; as awoman gets older, her risk of developing breast cancer increases. The following table shows the average percentage of American women in each
Prostate-specific antigen (PSA) is a protein produced by the cells of the prostate gland. Blood PSA level is often elevated in men with prostate cancer, but a number of benign (not cancerous)
One of the earliest models for the genetics of eye color was developed in 1907, and proposed a single-gene inheritance model, for which brown eye color is always dominant over blue eye color. Suppose
Australian cattle dogs are known to have a high prevalence of congenital deafness. Deafness in both ears is referred to as bilateral deafness, while deafness in one ear is referred to as unilateral
Consider the following card game with a well-shuffled deck of cards. If you draw a red card, you win nothing. If you get a spade, you win $\$ 5$. For any club, you win $\$ 10$ plus an extra \(\$
Gull clutch size. Large black-tailed gulls usually lay one to three eggs, and rarely have a fourth egg clutch. It is thought that clutch sizes are effectively limited by how effectively parents can
Ice cream usually comes in 1.5 quart boxes (48 fluid ounces), and ice cream scoops hold about 2 ounces. However, there is some variability in the amount of ice cream in a box as well as the amount of
When patients receive blood transfusions, it is critical that the blood type of the donor is compatible with the patients, or else an immune system response will be triggered. For example, a patient
Hepatitis C is spread primarily through contact with the blood of an infected person, and is nearly always transmitted through needle sharing among intravenous drug users. Suppose that in a month's
Approximately 12,500 stocks of Drosophila melanogaster flies are kept at The Bloomington Drosophila Stock Center for research purposes. A 2006 study examined how many stocks were infected with
Hyponatremia (low sodium levels) occurs in a certain proportion of marathon runners during a race. Suppose that historically, the proportion of runners who develop hyponatremia is 0.12. In a certain
Consider a senior Statistics concentrator with a packed extracurricular schedule, taking five classes, and writing a thesis. Each time she takes an exam, she either scores very well (at least two
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
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
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
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
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
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
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
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
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
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
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
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
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.
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
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.
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
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
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
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
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
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
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
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)
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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

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