8.10: Practice and Exploration

1. The data in the Table 8.4 represent the entire population of workers at a small industrial plant. The information included in the table corresponds to the employee identification number, age, gender identity, race or ethnicity, and hourly wage of those employed at the company. Write the employee identification number of each employee on separate index cards. Shuffle the cards a few times and then pick the first five cards from the top. The employees corresponding to these identification numbers are an approximate simple random sample of employees from the company. Compute the percentage of each gender identity in the population and in the sample. Are the population and sample percentages approximately the same? Compute the percentage of each race or ethnicity in the population and in the sample. Are the population and sample percentages approximately the same? What do these results say about the representativeness of the sample that you took?

Table 8.4 The population data for the employees at a small industrial plant. Gender identities are coded as F (female), M (male), and N (nonbinary). Race and ethnicities are coded as AA (African American), AS (Asian), HI (Hispanic), NA (Native American), and WH (White). Salary refers to the hourly salary of the employee.

Number	Age	Gender	Race	Salary
085	55	M	WH	26.52
359	21	N	HI	16.50
246	57	F	HI	21.95
589	25	F	WH	21.00
168	54	M	AS	25.75
204	33	F	HI	20.80
242	52	M	WH	26.45
908	48	M	WH	26.20
033	43	M	WH	26.65
591	31	F	WH	20.45
259	34	F	NA	15.90
498	22	F	WH	19.20
068	48	M	HI	21.65
729	38	F	AA	14.95
433	23	F	WH	26.85
544	31	F	AA	18.20
197	50	M	WH	28.00
414	54	M	WH	26.70
570	57	M	WH	28.80
004	61	F	AA	23.10
014	65	M	WH	30.55
814	65	F	WH	20.80
225	41	M	WH	21.00
423	25	M	WH	26.50
139	64	F	AA	23.60
632	41	M	HI	23.45
071	35	F	HI	23.20
502	51	F	HI	25.55
602	61	M	WH	27.60
464	25	F	AA	15.55
335	34	M	WH	27.05
724	25	F	AA	22.40
628	30	F	AA	15.90
597	34	N	HI	19.90
155	26	F	WH	25.20

2. A student at a small college wants to take a simple random sample of the students at the college. They decide that they will go to the common lunchroom at noon and wait until it is very crowded. They will then randomly pick students based on the available seats in the lunchroom using a simple random sample. Do you think that the resulting sample will be a simple random sample of students at the college? Why or why not?

3. A researcher is interested in establishing a political profile of residents in a large city. To gather data, they decide to stand in front of an independent bookstore with the hope of interviewing residents who are planning to visit the bookstore. Do you think the resulting sample will be representative of the population of residents in the city? Why or why not?

4. A researcher wishes to sample people for a survey as they enter a small political rally. As there is only one entrance, they seat themselves by the door and as each person enters, they flip a coin. If the coin flip shows heads, the person is directed to fill out a survey before entering. Otherwise, the person is not selected, and they can enter the rally without filling out the survey. Will this result in a simple random sample of those attending the rally? Why or why not?

5. A researcher intends to study the number of campus services that students at a large university use with the hopes of testing hypotheses about possible differences due to gender, race, and ethnicity, and sexual orientation. Using the semester schedule, the researcher decides to take a cluster sample with the classes taken to be the clusters. The researcher will then obtain the course roster for a random sample of classes. Within each of these classes, they will then take a random sample of students within each class. Do you think that using the classes as clusters is reasonable for this study? Why or why not?

6. The manager of a community center would like to survey its patrons about what additional needs the center could fulfill. The center offers lunch to those who live in the downtown area at noon, and so they go at lunchtime and randomly select twenty individuals using a simple random sample from those at lunch to take a survey. Do you think that this sample will be representative of the population? Why or why not?

7. The superintendent of a local school district is worried that non-white students in the school district are not being educated to the same level as the white students, creating an achievement gap that the school district must address. To study this issue the superintendent takes a simple random sample of ten students from each school in the district to be included in a study of educational achievement. What type of sampling method is the superintendent using?

8. A professor at a large private university is interested in studying gender pay gaps at their university. Because salary data is not available to them, they decide to randomly sample ten departments on campus and take a simple random sample of five faculty within each department. They will then email these faculty and ask them their salary and other relevant demographic information as part of a survey. What type of sampling method is this? Do you think there will be a problem with non-response? Could the faculty who decide not to take part in the survey be different from those who do in terms of salary?

9. The human resources department of a large company is interested in assessing whether discrimination against members of the LGBTQIA+ community is common at the company. To study this issue the director of the department proposes setting up an office where members of this community can come speak with counselors who will gather their information and assess the discrimination level for that individual. These interviews are to take place during normal working hours, so individuals who wish to participate will need to notify their supervisor that they will be taking part in the study. Do you think this study will have a problem with non-response? Do you think individuals who do not respond to the survey will be different from those who respond? In what ways? Can you propose a better way of getting people to participate in the study?

10. The manager of a survey organization has been put in charge of a survey of potential voters in the mayoral election in a large city. The current mayor has been critical of some of the practices of the police force regarding interactions with people of color. The survey has been designed to measure how this may change support for the mayor as a candidate in an upcoming reelection campaign. The survey will be implemented online, and the manager is aware of the need for a good response rate. The online interface used the title “Opinion Poll on the Policies of the Mayor.” The manager argues that this title is too boring and that people will not wish to participate in the survey as a result. The manager suggests the alternate title “Do You Care that the Mayor Keeps Criticizing the Police?” Do you think that this new title will increase the response rate? How might this new title affect the participation rate of those who support the mayor? How about those who do not support the mayor? Do you think the title change is a good idea? Why or why not?

11. Think again about the example of the puzzle described in earlier in this chapter. You are shown a fully assembled 1,000-piece puzzle, and you are asked to take a sample of 100 pieces in such a way that another person would have the best chance possible of guessing what the puzzle picture is without seeing the completed puzzle. How would you pick the 100 pieces? Would you use a simple random sample? Would you purposely choose pieces that best represent the picture, or give clues as to what the puzzle depicts? How does this situation differ from choosing individuals in a population for a survey?

12. In Problem 11 you are asked to take a sample of 100 puzzle pieces in such a way that another person would have the best chance possible of guessing what the picture is without seeing the completed puzzle. Now suppose the puzzle was lying flat on its face so that you could not see the picture, only the back of the puzzle. Now how would you pick the 100 pieces? Would you use a simple random sample? How does this situation differ from the one described in Problem 11? Is this situation closer to that of choosing individuals in a population for a survey? How does it differ?

13. Using an online news service, find a news article about an issue that is important to you personally 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 and how that information is gathered. Was a random sampling procedure used? If so, what type of random sampling technique was used? If a random sampling procedure was not used, then how was the data gathered? Do you think the sample is representative? Do you think there may be a problem with bias from non-response?

14. Using a library database, find an academic research article about an issue that is important to you personally that is based on an empirical analysis. Identify, as clearly as you can, the population that the authors of the research article have used to observe their data and gather information and how that information is gathered. Was a random sampling procedure used? If so, what type of random sampling technique was used? If a random sampling procedure was not used, then how was the data gathered? Do you think the sample is representative? Do you think there may be a problem with bias from non-response?