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Chapter 12: Problem 36

Consider each of these situations. Do you think the proposed sampling method is appropriate? Explain. a) We want to know if there is neighborhood support to turn a vacant lot into a playground. We spend a Saturday afternoon going door-to-door in the neighborhood, asking people to sign a petition. b) We want to know if students at our college are satisfied with the selection of food available on campus. We go to the largest cafeteria and interview every 10 th person in line.

Short Answer

Expert verified
Neither sampling method is entirely appropriate due to potential bias. They may not fully represent the opinions of the entire population in question.

Step by step solution

01

Assessing Sampling Method for Situation (a)

In situation (a), the proposed sampling method involves going door-to-door in one neighborhood on a Saturday afternoon to gather signatures for a petition regarding converting a vacant lot into a playground. This method can be effective for gauging local support if most residents are home during the survey period. However, it may not provide a complete picture since it could miss people who are not at home or those who do not typically stay in the neighborhood during weekends, thus introducing bias.
02

Assessing Sampling Method for Situation (b)

In situation (b), interviews are conducted with every 10th person in line at a large cafeteria to gauge student satisfaction with campus food selection. This method may be biased as it only samples those who are present in that specific cafeteria, potentially excluding students who do not frequent that cafeteria or have different food preferences. The timing and location of the sampling could affect the results, hence not representing the entire student body effectively.
03

Overall Appropriateness

For both situations, while the sampling methods might provide some insights, they are not entirely appropriate for obtaining a representative sample of the entire population in question. Situation (a) could miss diverse views as it focuses on one neighborhood and at one specific time. Situation (b) may miss opinions from students who avoid that specific cafeteria or are absent at the time of sampling, thus leading to biased results.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Bias in Sampling
When collecting data, it's crucial to ensure that the sampling method employed does not introduce bias. Bias occurs when certain groups within a population are over or under-represented. In our exercises, biases are evident in both sampling scenarios:
  • In situation (a), the timing and location of the door-to-door survey could exclude individuals who are not at home during the afternoon, such as those working on Saturdays or frequently traveling. This results in missing the opinions of a segment of the neighborhood, leading to potential bias in the findings.
  • In situation (b), interviewing every 10th person at a single cafeteria might not represent the full spectrum of culinary preferences among the students, especially if some students prefer other dining facilities or opt for off-campus dining options. This select group might share similar dining habits that do not reflect the overall sentiment of the student body.
To minimize bias, researchers should diversify their data collection approaches and ensure they reach all potential subgroups within the population. This might involve sampling at different times, locations, or using varied methods to capture a truly representative view.
Representative Sample
A representative sample accurately reflects the characteristics of the population from which it is drawn. It's essential for any survey or study to achieve credibility in its results. In the provided exercises, neither sampling method guarantees a truly representative sample due to their inherent limitations.
  • In situation (a), only those present in the neighborhood during the weekend are surveyed. This means that the opinions of individuals who are routinely away or traveling, as well as those who might not be engaged in neighborhood affairs, are missing. Ideally, a representative sample would capture inputs from all demographic and socio-economic segments of the neighborhood.
  • In situation (b), focusing on a single meal service location at one type of dining facility restricts the feedback to certain dining habits and preferences. A representative survey would incorporate responses from multiple dining venues and times, ensuring that every segment of campus diners is included.
Ensuring a representative sample requires careful planning and execution of the sampling method to include diverse inputs from all relevant parts of the population, thereby enhancing the reliability of the results.
Survey Methodology
Survey methodology is the framework through which data is collected, ensuring that results are valid, reliable, and as free from bias as possible. A well-developed methodology considers various factors, including the who, what, when, where, and how of data collection.
  • Who: In situation (a), identifying all resident types in the neighborhood and ensuring they're all given an opportunity to participate would be critical. This means potentially reaching out at varying times or through alternative channels, such as online surveys, to engage those not at home.
  • What: Situation (b) requires understanding of the full range of dining options and student preferences. The survey questions should be comprehensive, covering different dining experiences and locations on campus.
  • When and Where: Timing and location greatly affect the data collected. Both scenarios illustrate that limiting surveys to certain times and locations can skew data. Expanding the survey to different cafeterias at various times, as in Situation (b), would offer a broader view.
  • How: Using a mix of survey methods, such as online forms, face-to-face interviews, and telephonic surveys, can help gather a wide array of participant responses and ensure anyone can participate regardless of their situation at a single point in time.
A thorough consideration of these elements will strengthen the survey's methodology, creating results that are both meaningful and actionable. By overcoming the inherent biases and limitations of the initially proposed methods, the overall accuracy and applicability of the survey findings improve.

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Most popular questions from this chapter

What about drawing a random sample only from cell phone exchanges? Discuss the advantages and disadvantages of such a sampling method compared with surveying randomly generated telephone numbers from non-cell phone exchanges. Do you think these advantages and disadvantages have changed over time? How do you expect they'll change in the future?

A local TV station conducted a "PulsePoll" about the upcoming mayoral election. Evening news viewers were invited to phone in their votes, with the results to be announced on the latenight news. Based on the phone calls, the station predicted that Amabo would win the election with \(52 \%\) of the vote. They were wrong: Amabo lost, getting only \(46 \%\) of the vote. Do you think the station's faulty prediction is more likely to be a result of bias or sampling error? Explain.

An amusement park has opened a new roller coaster. It is so popular that people are waiting for up to 3 hours for a 2 -minute ride. Concerned about how patrons (who paid a large amount to enter the park and ride on the rides) feel about this, they survey every 10 th person on the line for the roller coaster, starting from a randomly selected individual. a) What kind of sample is this? b) What is the sampling frame? c) Is it likely to be representative?

The Web site www.gamefaqs.com asked, as their question of the day to which visitors to the site were invited to respond, \({ }^{4}\) Do you ever use emoticons when you type online? "Of the 87,262 respondents, \(27 \%\) said that they did not use emoticons. a) What kind of sample was this? b) How much confidence would you place in using \(27 \%\) as an estimate of the fraction of people who use emoticons?

Occasionally, when I fill my car with gas, I figure out how many miles per gallon my car got. I wrote down those results after 6 fill-ups in the past few months. Overall, it appears my car gets \(28.8\) miles per gallon. a) What statistic have I calculated? b) What is the parameter I'm trying to estimate? c) How might my results be biased? d) When the Environmental Protection Agency (EPA) checks a car like mine to predict its fuel economy, what parameter is it trying to estimate?
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