Linear Regression
Two-Way Tables
Sampling Design
Experimental Design
Ethics
100
Online advertisements contained pictures of diamond rings and listed their prices, diamond weights (in carats), and gold purity. Based on data for only the 18-carat gold ladiesʼ rings in the advertisements, the least-squares regression line for predicting price (in dollars) from the weight of the diamond (in carats) is
price = -6047.75 + 11975.14 carats
What is the predicted price when number of carats = 3?
$29877.67
100
Define Simpson's paradox.
Data shows one result as a whole, but different results when split into subcategories.
100
A universityʼs housing and residence office wants to know how much students pay per month for rent in off-campus housing. The university does not have enough on-campus housing for students, and this information will be used in a brochure about student housing. The housing office obtains a list of the 12,304 students who live in off-campus housing and have not yet graduated and mails a questionnaire to a randomly selected group of 200 of these students. Only 78 questionaires are returned. The important message in this problem is that the sample can redefine the population about which information is obtained.
Identify the population and the sample.
The population is (all) college students who live in off-campus housing.
The sample is the 78 students who live in off-campus housing and returned the questionnaire.
100
Is this an observational study or an experiment? What are the explanatory and response variables?
Many studies have found an association between red meat consumption and an increased risk of chronic diseases. What is the relationship between red meat consumption and mortality? A large study followed 120,000 men and women who were free of coronary heart disease and cancer at the beginning of the study. Participants were asked detailed questions about their eating habits every 4 years, and the study spanned almost 30 years. It was found that the risk of dying at an early age—from heart disease, cancer, or any other cause, rises with the amount of red meat consumed.
This is an observational study; the subjects chose their own “treatments” (how much red meat to eat). The explanatory variable is red meat consumption, and the response variable is whether or not a subject dies.
100
What organization reviews statistical studies to make sure the rights of each subject are protected?
Institutional Review Board
200
We expect a carʼs highway gas mileage to be related to its city gas mileage (in miles per gallon, mpg). Data for all 1259 vehicles in the governmentʼs 2019 Fuel Economy Guide give the regression line
highway mpg = 8.720 + (0.914 × city mpg)
for predicting highway mileage from city mileage.
Explain what the slope means in context of the problem.
The slope is 0.914. On average, highway mileage increases by 0.914 mpg for each additional 1-mpg change in city mileage.
200
0.402
200
Identify the sampling method.
In a poll conducted by a certain research center, 757 adults were called after their telephone numbers were randomly generated by a computer, and 6 % were able to correctly identify the secretary of state.
Random sampling
200
Identify the subjects, factors, and treatments, and response variable.
Adolescent obesity is a serious health risk affecting more than 5 million young people in the United States alone. Laparoscopic adjustable gastric banding has the potential to provide a safe and effective treatment. Fifty adolescents between 14 and 18 years old with a body mass index higher than 35 were recruited from the Melbourne, Australia, community for the study. Twenty-five were randomly selected to undergo gastric banding, and the remaining 25 were assigned to a supervised lifestyle intervention program involving diet, exercise, and behavior modification. All subjects were followed for two years, and their weight loss was recorded.
Subjects: the 50 obese adolescents. Factor: type of intervention.
Treatments:gastric banding operation or supervised lifestyle intervention.
Response variable: weight loss.
200
Define informed consent.
Subjects are informed of all possible risks and consequences of participating in an experiment and then give written consent to participate.
300
For a relationship between diamond price and carrat size, r2=0.76. Interpret this in context of the problem.
76% of the variation in diamond price can be explained by the model.
300
0.976
300
Identify the sampling method.
A woman is selected by a marketing company to participate in a paid focus group. The company says that the woman was selected because every 1000th person in the phone number listing was being selected.
Systematic
300
What kind of blinding is used?
Researchers are testing a new drug. They randomly assign subjects in to a control (placebo) group and a treatment group. Researchers are aware of which subjects were placed in which group.
Single-blind
300
Is informed consent required if there are only benefits to a study?
No
400
The mean height of American women in their twenties is about 64.3 inches, and the standard deviation is about 2.7 inches. The mean height of men the same age is about 69.9 inches, with standard deviation about 3.1 inches. Suppose that the correlation between the heights of husbands and wives is about r = 0.5.
Find the slope of the linear regression line.
0.574
400
What marginal and/or conditional distributions would you use to determine what percent of all those who have read the book have also watched the movie?
Marginal distribution of "read the book," conditional distribution of "watched the movie"
400
A study in El Paso, Texas, looked at seat belt use by drivers. Drivers were observed at randomly chosen convenience stores. After they left their cars, they were invited to answer questions that included questions about seat belt use. In all, 75% said they always used seat belts, yet only 61.5% were wearing seat belts when they pulled into the store parking lots. Explain the type and reason for the bias observed in responses to the survey.
Response Bias: People probably claim to wear their seat belts because they know they should (and it is the law); they may be embarrassed or ashamed to say that they do not always wear seat belts.
400
What kind of experiment is this?
An educational study evaluating the two teaching methods where students are matched based on their baseline test scores. The Wilcoxon Signed-Rank Test is used to the analyze the performance improvements.
Matched pairs experiment
400
Define confidentiality.
All data about a subject will be kept confidential, even when published.
500
Draw a residual plot of a scenario that is modeled well by a linear regression model.
500
Sampling Design Question! Identify the form of bias.
A radio show asks people to call in and express their opinions about a recent bill that has been passed in the Senate. All of those who call in express strong support or strong opposition to the bill.
Voluntary response bias
500
A firm wants to understand the attitudes of its minority managers toward its system for assessing management performance. Following is a list of all the firmʼs managers who are members of minority groups. Explain a strategy for randomly picking 4 managers
Adelaja Draguljic Huo Modur
Ahmadiani Fernandez Ippolito Rettiganti
Barnes Fox Jiang Rodriguez
Bonds Gao Jung Sanchez
Burke Gemayel Mani Sgambellone
Deis Gupta Mazzeo Yajima
Ex 1: Assigning each name as 2 digit number and putting it in a randomizer. Pick the first four names
06 = Deis, 08 = Fernandez, and 11 = Gemayel.
Ex 2: Put names in a hat, draw the first for names
500
A randomized experiment where the subjects are randomly assigned to two or more treatment groups. Students learn how to drive, either taught by a driving instructor (treatment 1) or being self-taught by watching YouTube videos (treatment 2). The results are measured to see the difference.
Randomized Comparative Experiment
500
What types of studies require review for the IRB?
Studies that involve human subjects