Questions and Answers of Descriptive Statistics

A linear model fit to RFFT scores and age for 500 randomly sampled individuals from the PREVEND data has equation $\widehat{R F F T}=137.55-1.26($ Age).(a) Interpret the slope and intercept values
According to a report on sleep deprivation by the Centers for Disease Control and Prevention, the proportion of California residents who reported insufficient rest or sleep during each of the
Cardiopulmonary resuscitation (CPR) is a procedure commonly used on individuals suffering a heart attack when other emergency resources are not available. This procedure is helpful in maintaining
Red-green colorblindness is a commonly inherited form of colorblindness; the gene involved is transmitted on the X chromosome in a recessive manner. If a male inherits an affected X chromosome, he is
The most common form of colorblindness is a recessive, sex-linked hereditary condition caused by a defect on the X chromosome. Females are XX, while males are XY. Individuals inherit one chromosome
Sex linkage refers to the inheritance pattern that results from a mutation occurring on a gene located on a sex chromosome. A classic example of a sex-linked trait in humans is red-green color
The following are cutoff values for the upper 5% of a $t$-distribution with either degrees of freedom 10, 50 , or 100: $2.23,1.98$, and 2.01. Identify which value belongs to which distribution
Researchers interested in lead exposure due to car exhaust sampled the blood of 52 police officers subjected to constant inhalation of automobile exhaust fumes while working traffic enforcement in a
Researchers collected a simple random sample of 36 children who had been identified as gifted in a large city. The following histograms show the distributions of the IQ scores of mothers and fathers
Suppose that you are interested in determining whether exposure to the organochloride DDT, which has been used extensively as an insecticide for many years, is associated with breast cancer in women.
It is hypothesized that the blue-green color of the eggshells of many avian species represents an informational signal as to the health of the female that laid the eggs. To investigate this
A diamond's price is determined by various measures of quality, including carat weight. The price of diamonds increases as carat weight increases. While the difference between the size of a 0.99
In a study examining 131 collared flycatcher eggs, researchers measured various characteristics in order to study their relationship to egg size (assayed as egg volume, in $\mathrm{mm}^{3}$ ).
The table provides summary statistics on highway fuel economy of cars manufactured in 2012. Use these statistics to calculate a $98 \%$ confidence interval for the difference between average
While placebo treatment can influence subjective symptoms, it is typically believed that patient response to placebo requires concealment or deception; in other words, a patient must believe that
In Exercises 5.29 and 5.31 we compared the effects of two types of feed at a time. A better analysis would first consider all feed types at once: casein, horsebean, linseed, meat meal, soybean, and
The China Health and Nutrition Survey aims to examine the effects of the health, nutrition, and family planning policies and programs implemented by national and local governments. It, for example,
Guppies are small, brightly colored tropical fish often seen in freshwater fish aquariums. A study was conducted in 147 male guppies to examine the relationship between coloration and heterozygosity;
Exercise 6.10 showed a plot of length versus height for 147 male guppies with a least squares regression line.(a) Identify two points that have relatively high leverage and discuss whether these
The residual plots below are for the linear model fit in Exercise 6.10 predicting length from height for 147 male guppies.(a) From a plot of residual values versus predicted values, are the
Multilocus heterozygosity (MLH) is reflective of genetic quality; according to sexual selection research, it is thought that sexual ornamentation functions as a visual indicator of fitness. By
Exercise 5.24 introduced data on the price of diamonds based on whether a diamond is 0.99 carats or 1 carat. Based on the summary statistics, write an estimated model equation predicting price from a
Exercise 5.28 introduced data from an analysis investigating whether hatch weights between transgenic and non-transgenic chicks differ.(a) Write an estimated least squares regression line for a model
Exercise 6.20 introduced a linear model for predicting relative orange area from proportion of loci that are heterozygous (MLH). Relative orange area refers to the percentage of the body that is
The following regression output is for predicting RFFT score of 500 randomly sampled individuals from the PREVEND data based on age (years).(a) Do these data provide statistically significant
Exercise 5.28 introduced data from an analysis investigating whether hatch weights between transgenic and non-transgenic chicks differ. Based on the results from conducting the twogroup test, explain
Exercise 6.27 introduces data from a random sample of 170 married couples in Britain, where both partners' ages are below 65 years, and fits a model predicting wife's age from husband's age. Wife's
The relationship between length and height for 147 male guppies was introduced in Exercise 6.10, which used the summary statistics to calculate the equation of the least squares line for length as a
The summary table below shows the results of a multiple regression model of RFFT score versus statin use and age.In a clinical setting, the interpretive focus lies on reporting the nature of the
Can the results of the analysis in Exercise 7.1 be used to conclude that as one ages, one's cognitive function (as measured by RFFT score) declines? Explain your answer.Data From Exercise 7.1 7.1
Wolbachia is a microbial symbiont estimated to be hosted by about $40 \%$ of all arthropod species, transmitted primarily from females to their offspring through the eggs. Researchers conducted a
A model was fit for a random sample of 100 low birth weight infants born in two teaching hospitals in Boston, Massachusetts, regressing birthweight on the predictors gestational age and toxemia
One research question of public health interest is to determine the extent to which high blood pressure is a genetic phenomenon. In 20 families, the systolic blood pressure of the mother, father, and
Exercise 7.4 introduced a study about Wolbachia and reproductive success in a wasp host. The following table shows the model coefficients for a model predicting the number of eggs laid over a
A study was conducted at a university outpatient primary care clinic in Switzerland to identify factors associated with difficult doctor-patient encounters. The data consist of 527 patient
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

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