Questions and Answers of OpenIntro Statistics

A market researcher wants to evaluate car insurance savings at a competing company. Based on past studies he is assuming that the standard deviation of savings is $100. He wants to collect data such
The standard deviation of SAT scores for students at a particular Ivy League college is 250 points. Two statistics students, Raina and Luke, want to estimate the average SAT score of students at this
The General Social Survey collects data on demographics, education, and work, among many other characteristics of US residents. Using ANOVA, we can consider educational attainment levels for all
Air quality measurements were collected in a random sample of 25 country capitals in 2013, and then again in the same cities in 2014. We would like to use these data to compare average air quality
Caffeine is the world's most widely used stimulant, with approximately 80% consumed in the form of coffee. Participants in a study investigating the relationship between coffee consumption and
A professor who teaches a large introductory statistics class (197 students) with eight discussion sections would like to test if student performance differs by discussion section, where each
Determine if the following statements are true or false. If false, explain. (a) In a paired analysis we first take the difference of each pair of observations, and then we do inference on these
In each of the following scenarios, determine if the data are paired. (a) Compare pre- (beginning of semester) and post-test (end of semester) scores of students. (b) Assess gender-related
In each of the following scenarios, determine if the data are paired. (a) We would like to know if Intel's stock and Southwest Airlines' stock have similar rates of return. To find out, we take
When doing an ANOVA, you observe large differences in means between groups. Within the ANOVA framework, this would most likely be interpreted as evidence strongly favoring the
Determine if the following statements are true or false, and explain your reasoning for statements you identify as false. (a) When comparing means of two samples where n1 = 20 and n2 = 40, we
Subjects from Central Prison in Raleigh, NC, volunteered for an experiment involving an "isolation" experience. The goal of the experiment was to find a treatment that reduces subjects' psychopathic
A large farm wants to try out a new type of fertilizer to evaluate whether it will improve the farm's corn production. The land is broken into plots that produce an average of 1,215 pounds of corn
A medical research group is recruiting people to complete short surveys about their medical history. For example, one survey asks for information on a person's family history in regards to cancer.
Undergraduate students taking an introductory statistics course at Duke University conducted a survey about GPA and major. The side-by-side box plots show the distribution of GPA among three groups
A study suggests that the average college student spends 10 hours per week communicating with others online. You believe that this is an underestimate and decide to collect your own sample for a
A college counselor is interested in estimating how many credits a student typically enrolls in each semester. The counselor decides to randomly sample 100 students by using the registrar's database
The National Survey of Family Growth conducted by the Centers for Disease Control gathers information on family life, marriage and divorce, pregnancy, infertility, use of contraception, and men's and
We would like to test if students who are in the social sciences, natural sciences, arts and humanities, and other fields spend the same amount of time studying for this course. What type of test
Exercise 7.56 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 thinks this value has changed since the survey
A study compared five different methods for teaching descriptive statistics. The five methods were traditional lecture and discussion, programmed textbook instruction, programmed text with lectures,
For each of the six plots, identify the strength of the relationship (e.g. weak, moderate, or strong) in the data and whether fitting a linear model would be reasonable. (a) (d) (e) (c) (f)
The two scatterplots below show the relationship between final and mid-semester exam grades recorded during several years for a Statistics course at a university.(a) Based on these graphs, which of
The scatterplots shown below each have a superimposed regression line. If we were to construct a residual plot (residuals versus x) for each, describe what those plots would look like. (a) (b)
The Great Britain Office of Population Census and Surveys once collected data on a random sample of 170 married couples in Britain, recording the age (in years) and heights (converted here to inches)
Determine if the following statements are true or false in ANOVA, and explain your reasoning for statements you identify as false.(a) As the number of groups increases, the modified significance
For each of the six plots, identify the strength of the relationship (e.g. weak, moderate, or strong) in the data and whether fitting a linear model would be reasonable. (d) (b) (e) (c) (f)
Determine if the following statements are true or false, and explain your reasoning for statements you identify as false. If the null hypothesis that the means of four groups are all the same is
Shown below are two plots of residuals remaining after fitting a linear model to two different sets of data. Describe important features and determine if a linear model would be appropriate for these
Match each correlation to the corresponding scatterplot.(a) R = -0:7(b) R = 0:45(c) R = 0:06(d) R = 0:92 (1) (2) (3) (4)
A group of researchers are interested in the possible effects of distracting stimuli during eating, such as an increase or decrease in the amount of food consumption. To test this hypothesis, they
Match each correlation to the corresponding scatterplot.(a) R = 0:49(b) R = -0:48(c) R = -0:03(d) R = -0:85 (1) (2) (3) (4)
The researchers from Exercise 7.47 also investigated the effects of being distracted by a game on how much people eat. The 22 patients in the treatment group who ate their lunch while playing
Determine if the following statement is true or false, and if false, explain your reasoning: If comparing means of two groups with equal sample sizes, always use a paired test.
The Coast Starlight Amtrak train runs from Seattle to Los Angeles. The scatterplot below displays the distance between each stop (in miles) and the amount of time it takes to travel from one stop to
1,302 UCLA students were asked to fill out a survey where they were asked about their height, fastest speed they have ever driven, and gender. The scatterplot on the left displays the relationship
The distribution of the number of eggs laid by a certain species of hen during their breeding period has a mean of 35 eggs with a standard deviation of 18.2. Suppose a group of researchers randomly
At a startup company running a new weather app, an engineering team generally runs experiments where a random sample of 1% of the app's visitors in the control group and another 1% were in the
A study conducted at the University of Denver investigated whether babies take longer to learn to crawl in cold months, when they are often bundled in clothes that restrict their movement, than in
Researchers studying anthropometry collected body girth measurements and skeletal diameter measurements, as well as age, weight, height and gender for 507 physically active individuals. The
The scatterplot below shows the relationship between weight measured in kilograms and hip girth measured in centimeters from the data described in Exercise 8.13.(a) Describe the relationship between
The following regression output is for predicting the heart weight (in g) of cats from their body weight (in kg). The coefficients are estimated using a dataset of 144 domestic cats.(a) Write out the
The following regression output is for predicting annual murders per million from percentage living in poverty in a random sample of 20 metropolitan areas.(a) Write out the linear model.(b) Interpret
The Association of Turkish Travel Agencies reports the number of foreign tourists visiting Turkey and tourist spending by year. Three plots are provided: scatterplot showing the relationship between
The scatterplot below shows the relationship between the number of calories and amount of carbohydrates (in grams) Starbucks food menu items contain. Since Starbucks only lists the number of calories
Identify the outliers in the scatterplots shown below, and determine what type of outliers they are. Explain your reasoning. (a) (b) வெளியத்தியைக்
Eduardo and Rosie are both collecting data on number of rainy days in a year and the total rainfall for the year. Eduardo records rainfall in inches and Rosie in centimeters. How will their
Identify the outliers in the scatterplots shown below and determine what type of outliers they are. Explain your reasoning. (a) (b) ਸ (c)
The scatterplot below shows the percent of families who own their home vs. the percent of the population living in urban areas. There are 52 observations, each corresponding to a state in the US.
Exercise 8.25 presents regression output from a model for predicting annual murders per million from percentage living in poverty based on a random sample of 20 metropolitan areas. The model output
Many college courses conclude by giving students the opportunity to evaluate the course and the instructor anonymously. However, the use of these student evaluations as an indicator of course quality
Exercise 8.33 presents a scatterplot displaying the relationship between husbands' and wives' ages in a random sample of 170 married couples in Britain, where both partners' ages are below 65 years.
Many people believe that gender, weight, drinking habits, and many other factors are much more important in predicting blood alcohol content (BAC) than simply considering the number of drinks a
What would be the correlation between the ages of husbands and wives if men always married woman who were(a) 3 years younger than themselves?(b) 2 years older than themselves?(c) half as old as
Exercise 9.3 presents a regression model for predicting the average birth weight of babies based on length of gestation, parity, height, weight, and smoking status of the mother. Determine if the
The scatterplot below summarizes husbands' and wives' heights in a random sample of 170 married couples in Britain, where both partners' ages are below 65 years. Summary output of the least squares
What would be the correlation between the annual salaries of males and females at a company if for a certain type of position men always made(a) $5,000 more than women?(b) 25% more than women?(c) 15%
Consider a regression predicting weight (kg) from height (cm) for a sample of adult males. What are the units of the correlation coefficient, the intercept, and the slope?
The scatterplot and least squares summary below show the relationship between weight measured in kilograms and height measured in centimeters of 507 physically active individuals.(a) Describe the
Exercise 8.22 introduced a data set on nutrition information on Starbucks food menu items. Based on the scatterplot and the residual plot provided, describe the relationship between the protein
Determine if I or II is higher or if they are equal. Explain your reasoning. For a regression line, the uncertainty associated with the slope estimate, b1, is higher whenI. There is a lot of scatter
The scatterplots below show the relationship between height, diameter, and volume of timber in 31 felled black cherry trees. The diameter of the tree is measured 4.5 feet above the ground.(a)
Suppose we fit a regression line to predict the shelf life of an apple based on its weight. For a particular apple, we predict the shelf life to be 4.6 days. The apple's residual is -0.6 days. Did we
Exercise 8.26 presents regression output from a model for predicting the heart weight (in g) of cats from their body weight (in kg). The coefficients are estimated using a dataset of 144 domestic
Suppose we fit a regression line to predict the number of incidents of skin cancer per 1,000 people from the number of sunny days in a year. For a particular year, we predict the incidence of skin
Exercise 8.29 gives a scatterplot displaying the relationship between the percent of families that own their home and the percent of the population living in urban areas. Below is a similar
A logistic regression model was proposed for classifying common brushtail possums into their two regions in Exercise 9.15. The outcome variable took value 1 if the possum was from Victoria and 0
Exercise 9.4 provides regression output for the full model, including all explanatory variables available in the data set, for predicting the number of days absent from school. In this exercise we
Exercise 9.1 introduces a data set on birth weight of babies. Another variable we consider is parity, which is 1 if the child is the first born, and 0 otherwise. The summary table below shows the
Exercise 8.13 introduces data on shoulder girth and height of a group of individuals. The mean shoulder girth is 107.20 cm with a standard deviation of 10.37 cm. The mean height is 171.14 cm with a
The scatterplot shows the relationship between socioeconomic status measured as the percentage of children in a neighborhood receiving reduced-fee lunches at school (lunch) and the percentage of bike
Researchers interested in the relationship between absenteeism from school and certain demographic characteristics of children collected data from 146 randomly sampled students in rural New South
The common brushtail possum of the Australia region is a bit cuter than its distant cousin, the American opossum (see Figure 8.4 on page 307). We consider 104 brushtail possums from two regions in
Match each correlation to the corresponding scatterplot.(a) r = -0:72(b) r = 0:07(c) r = 0:86(d) r = 0:99 (1) (2) (3) (4)
Exercise 9.4 considers a model that predicts the number of days absent using three predictors: ethnic background (eth), gender (sex), and learner status (lrn). The table below shows the adjusted
The Child Health and Development Studies investigate a range of topics. One study considered all pregnancies between 1960 and 1967 among women in the Kaiser Foundation Health Plan in the San
Exercise 8.12 introduces data on the average monthly temperature during the month babies first try to crawl (about 6 months after birth) and the average first crawling age for babies born in a given
A FiveThirtyEight.com article reports that "Horror movies get nowhere near as much draw at the box office as the big-time summer blockbusters or action/adventure movies ... but there's a huge
Timber yield is approximately equal to the volume of a tree, however, this value is difficult to measure without first cutting the tree down. Instead, other variables, such as height and diameter,
On January 28, 1986, a routine launch was anticipated for the Challenger space shuttle. Seventy-three seconds into the flight, disaster happened: the shuttle broke apart, killing all seven crew
A survey of 55 Duke University students asked about their GPA, number of hours they study at night, number of nights they go out, and their gender. Summary output of the regression model is shown
The student from Exercise 9.14 analyzed return-on-investment (ROI) for movies based on release year and genre of movies. The plots below show the predicted ROI vs. actual ROI for each of the genres
Determine if the following statements are true or false. If false, explain why.(a) A correlation coefficient of -0.90 indicates a stronger linear relationship than a correlation of 0.5.(b)
Spam filters are built on principles similar to those used in logistic regression. We fit a probability that each message is spam or not spam. We have several email variables for this problem: to
Suppose a social scientist is interested in studying what makes audiences love or hate a movie. She collects a random sample of movies (genre, length, cast, director, budget, etc.) as well as a
Suppose an online media streaming company is interested in building a movie recommendation system. The website maintains data on the movies in their database (genre, length, cast, director, budget,
Determine which of the following statements are true and false. For each statement that is false, explain why it is false.(a) If predictors are collinear, then removing one variable will have no
Determine which of the following statements are true and false. For each statement that is false, explain why it is false.(a) Suppose we consider the first two observations based on a logistic
In Exercise 9.21, we encountered a data set where we applied logistic regression to aid in spam classification for individual emails. In this exercise, we've taken a small set of these variables and
For each of the following situations, state whether the parameter of interest is a mean or a proportion.(a) A poll shows that 64% of Americans personally worry a great deal about federal spending and
For each of the following situations, state whether the parameter of interest is a mean or a proportion. It may be helpful to examine whether individual responses are numerical or categorical.(a) In
Heights of 10 year olds, regardless of gender, closely follow a normal distribution with mean 55 inches and standard deviation 6 inches.(a) What fraction of 10 year olds are taller than 76 inches?(b)
Heights of 10 year olds, regardless of gender, closely follow a normal distribution with mean 55 inches and standard deviation 6 inches.(a) The height requirement for Batman the Ride at Six Flags
Suppose you're considering buying your expensive chemistry textbook on Ebay. Looking at past auctions suggests that the prices of this textbook follow an approximately normal distribution with mean
Heights of 10 year olds, regardless of gender, closely follow a normal distribution with mean 55 inches and standard deviation 6 inches.(a) What is the probability that a randomly chosen 10 year old
Suppose weights of the checked baggage of airline passengers follow a nearly normal distribution with mean 45 pounds and standard deviation 3.2 pounds. Most airlines charge a fee for baggage that
Pew Research reported that the typical response rate to their surveys is only 9%. If for a particular survey 15,000 households are contacted, what is the probability that at least 1,500 will agree to
The American Community Survey estimates that 47.1% of women ages 15 years and over are married.(a) We randomly select three women between these ages. What is the probability that the third woman
SAT scores (out of 1600) are distributed normally with a mean of 1100 and a standard deviation of 200. Suppose a school council awards a certificate of excellence to all students who score at least
Suppose a newspaper article states that the distribution of auto insurance premiums for residents of California is approximately normal with a mean of $1,650. The article also states that 25% of

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