4.9: Practice and Exploration
- Page ID
- 62847
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- The administration at a small college is interested in exploring how their current students feel about immigration issues, and in particular how gender and race might be associated with certain opinions about immigration issues. They would like to know what percentage of each race and gender combination support immigrant rights on campus. What is the population for this study? What variables do you think the study should include? What are the parameters of interest for this study? What issues of practicality might be of concern when conducting this study? Do you think the corresponding study will have limitations? What will they be?
- The president of the sociology club at a large university is interested in sponsoring an on-campus movie to help celebrate Black History Month. During a previous meeting of the club, three movies were selected as possible candidates for the event. The president of the club would like the event to be a success and is therefore worried about which movie to pick. The club decides to use a small survey to try to determine which movie would have the largest audience. Describe several populations the club might consider studying. How accessible are these populations? Do you think these populations could be studied from a practical viewpoint? Which of these populations do you think the club would be most interested in?
- Suppose that you are planning a research project that would investigate the association between the demographics of neighborhoods and their corresponding economic conditions. What established online databases maintained by the United States federal government do you think might be helpful with this research project? What types of data do you think you might be able to find in these databases? Can these databases be accessed by the public or is special access required?
- A small business has ten employees and is interested in their opinion of their working conditions. In this business there are two places where employees can interact with customers, either inside the office or at a kiosk outside the office. The business is worried that weather conditions make working outside in the kiosk less appealing to the employees. The following data is obtained from talking with each of the employees.
|
Employee |
Inside |
Outside |
|
1 |
6 |
5 |
|
2 |
10 |
7 |
|
3 |
10 |
6 |
|
4 |
10 |
8 |
|
5 |
6 |
2 |
|
6 |
2 |
1 |
|
7 |
2 |
3 |
|
8 |
5 |
2 |
|
9 |
10 |
4 |
|
10 |
9 |
9 |
In the data each worker rated, on a scale from 1 to 10, the working conditions inside and outside the business. For this rating scale a higher number indicates better working conditions. Of interest is the average rating for working outside subtracted from the average rating for working inside. Identify the variables in this population along with the parameter of interest. What is the value of the parameter? What does the value of the parameter say about the working conditions inside compared with the working conditions outside?
- Consider a court case where the plaintiffs allege that individuals who, subsequent to becoming employed at a company, identified themselves as having a nonbinary gender identity have not been subsequently promoted to higher positions in the company at the same rate as other employees. What would you consider the correct population to be for this type of litigation? Explain why you identified this population.
- Suppose that you are working for a friend who is running for election to a position in the local county government, which is in a rural county with a population of about 10,000. Your friend is a young, dynamic individual who has a keen interest in helping the young population in the area. Because of your interest in data, you are put in charge of studying the political affiliations and viewpoints of young people. Describe several populations you might consider studying and how the views of the corresponding populations might be of interest to your friend. How accessible are these populations? Do you think these populations could be studied from a practical viewpoint? Which of these populations do you think your friend would be most interested in?
- Consider a court case where an employer is accused of having a racial bias in their hiring practices for entry level positions that require a high school level education. The employer is a regional company that extends through several counties of their home state. What would you consider the correct population to be for this type of litigation? Explain why you identified this population.
- Many people collect things like vinyl records, baseball cards, stuffed animals, sneakers, and the like. If you have such a collection, think about that collection as a population. If you do not collect anything, think about a collection a friend or family member might have. Suppose that you wanted to summarize what is in the collection without having to describe each item separately. What would be the variables that one might be interested in and why? What population characteristics might one be interested in and why?
- An employer advertises for a position at a loading dock where applicants are required to be able to stack boxes onto a truck of a certain height, a requirement that is mentioned in the employment advertising. The employer is later sued by a group that states that the employer has biased hiring practices. In the past five years no applicants who have identified as female have been hired. In the case, the employer argues that the physical requirement for the position is the reason that no female applicants have been hired. If you were the lawyer for the plaintiffs, what population would you identify as being the correct relevant population of potential employees for this position? Why would you choose this population?
- While searching for medical information on the dangers of vapor-based tobacco products, you come across a study that describes the use of vape products across different age groups, race and ethnic groups, and gender identities. The research is from a well-respected group of academic researchers. What type of government resources would have been helpful to the researchers in gathering data of this subject? What problems might they have encountered while trying to find their data and identify the relevant population? What limitations do you think the study might have?
- A city has recently invested in city-run youth centers—places where young people can go and play sports, play games, study, and relax away from home during non-school days. The founders of the program would like to assess if there is an association between the presence of these centers and the crime rates in the surrounding neighborhoods. Determine several ways that the population of interest can be identified for this problem. What type of government resources could have been helpful to the researchers in gathering data on this subject? What problems might they encounter while trying to find their data and identify the relevant population? What limitations do you think the study might have?
- Using an online news service, find a news article about an issue important to you that is based on an empirical analysis. Identify, as clearly as you can, the population that the authors of the news article have used to observe their data and gather information. Are the data they obtained based on information from government sources and databases? Are there stated limitations to the population in the new article? What are they? Are there other limitations in identifying the population that are not stated in the news article but which you think might present a problem? Why? Based on these answers, how reliable and universal do you think the conclusions of the news article are? Can you think of any ways to improve the research?
- Using an online source or your library, find an academic research article about an issue that is important to you. Identify, as clearly as you can, the population that the authors of the article have used to observe their data and gather information. Are the data they obtained based on information from government sources and databases? Are there stated limitations to the population in the article? What are they? Are there other limitations in identifying the population not stated in the article but which you think might present a problem? Why? Based on these answers, how reliable and universal do you think that the conclusions of the article are? Can you think of any ways to improve the research?
- Using an online source or your library, find information on a legal case that dealt with employment discrimination. What event occurred that gave rise to the case? If possible, determine the population used to decide the merits of the case. What was the result?

