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Chapter 11: Problem 20

\- Playground Some people have been complaining that the children's playground at a municipal park is too small and is in need of repair. Managers of the park decide to survey city residents to see if they believe the playground should be rebuilt. They hand out questionnaires to parents who bring children to the park. Describe possible biases in this sample.

Short Answer

Expert verified
The sample is biased as it only includes parents who visit the playground, potentially skewing opinions towards those who want improvements.

Step by step solution

01

Identify the Population

The goal of the survey is to gather opinions from city residents about whether the playground should be rebuilt. Therefore, the population of interest is all city residents, not just those who visit the park.
02

Define the Sample

The sample consists of parents who bring their children to the playground and are given the questionnaires. This group is a subset of the total city residents.
03

Examine Sampling Method

Since the questionnaires are only handed out at the playground to parents who visit, the sample is not randomly chosen from the entire population of city residents. This could introduce bias into the survey results.
04

Identify Potential Bias

Parents who bring their children to the playground are more likely to have stronger opinions about its condition because they use it regularly. This could lead to an overrepresentation of people who are more inclined to want improvements or repairs at the playground.
05

Consider Survey Reach

This sampling method excludes residents who do not use the park or who do not visit it regularly. They might still have opinions about the use of public funds or other priorities for the park, but these views would not be captured in this survey.

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Key Concepts

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

Sample Population
The sample population is a crucial concept when designing a survey as it directly affects the relevance and accuracy of the results. In our playground survey, the intended population is all city residents. This is because the decision about rebuilding affects the community as a whole.
  • However, the actual sample consists only of parents who visit the playground with their children.
This group is much smaller and more specific than the full population. It's important to note that the sample should ideally reflect the diversity of the entire population to get unbiased opinions.
Sampling Method
The sampling method involves the technique used to select the sample from the population. A common goal is to have a sample that accurately reflects the larger group, often achieved through random sampling.
  • In the playground case, questionnaires are only available at the playground, meaning the sample is not randomly selected from city residents.
  • Such a choice can lead to a non-representative sample because it systematically includes only those who are already playground users.
To improve, a better method would be to reach a broader group, perhaps through mail or online surveys accessible to all residents.
Potential Bias
Potential bias arises when certain factors skew the results of a survey. In this scenario, the bias is primarily due to the selection of participants. The parents who frequent the playground have their experiences, which are likely different from those who don鈥檛 visit the park.
  • They might have stronger preferences, especially towards reconstruction, due to direct and frequent encounters with the playground鈥檚 conditions.
  • This leads to an overrepresentation of these views, which doesn鈥檛 necessarily reflect how all city residents feel, potentially disregarding others' priorities or resource allocations.
Recognizing such biases is essential to ensure accurate assessment of public opinion.
Survey Reach
Survey reach concerns the extent to which various segments of the target population can participate in the survey. A broad reach ensures diverse input and a balanced understanding of public opinion.
  • In this exercise, the reach is limited to those already visiting the playground, missing out on input from residents who may have varied views or interests in public spending.
  • Residents who never visit may have useful insights or valid concerns about the allocation of city funds elsewhere.
Expanding reach could include utilizing multiple distribution channels such as online platforms or community events, ensuring more comprehensive feedback from all walks of city life.

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Most popular questions from this chapter

Gallup World At its website (www.gallupworldpoll com) the Gallup World Poll describes their methods. After one report they explained: Results are based on face-to-face interviews with randomly selected national samples of approximately 1,000 adults, aged 15 and older, who live permanently in each of the 21 sub-Saharan African nations surveyed. Those countries include Angola (areas where land mines might be expected were excluded), Benin, Botswana, Burkina Faso, Cameroon, Ethiopia, Ghana, Kenya, Madagascar (areas where interviewers had to walk more than 20 kilometers from a road were excluded), Mali, Mozambique, Niger, Nigeria, Senegal, Sierra Leone, South Africa, Tanzania, Togo, Uganda (the area of activity of the Lord's Resistance Army was excluded from the survey), Zambia, and Zimbabwe.... In all countries except Angola, Madagascar, and Uganda, the sample is representative of the entire population. a) Gallup is interested in sub-Saharan Africa. What kind of survey design are they using? b) Some of the countries surveyed have large populations. (Nigeria is estimated to have about 130 million people.) Some are quite small. (Togo's population is estimated at 5.4 million.) Nonetheless, Gallup sampled 1000 adults in each country. How does this affect the precision of its estimates for these countries?

\- Survey questions Examine each of the following questions for possible bias. If you think the question is biased, indicate how and propose a better question. a) Should companies that pollute the environment be compelled to pay the costs of cleanup? b) Given that 18 -year-olds are old enough to vote and to serve in the military, is it fair to set the drinking age at \(21 ?\)

Milk samples Dairy inspectors visit farms unannounced and take samples of the milk to test for contamination. If the milk is found to contain dirt, antibiotics, or other foreign matter, the milk will be destroyed and the farm reinspected until purity is restored. Would simple random sampling be appropriate for selecting farms for inspection? If so, explain how it would be done. If not, explain why it is not appropriate.

Toxic waste The Environmental Protection Agency took a map of a region near a former industrial waste dump and placed a grid of 552 squares on it. They randomly selected any 16 of those squares from which to collect soil samples and checked each for evidence of toxic chemicals. a) What type of sampling did they use? b) Is there any sort of bias associated with this sampling procedure? c) One researcher suggests that plots closer to the old dump site could contain more contaminants than those farther away. How could the sampling procedure be improved to take this into account

Phone surveys Anytime we conduct a survey, we must take care to avoid undercoverage. Suppose we plan to select 500 names from the city phone book, call their homes between noon and \(4 \mathrm{PM}\), and interview whoever answers, anticipating contacts with at least 200 people. a) Why is it difficult to use a simple random sample here? b) Describe a more convenient, but still random, sampling strategy. c) What kinds of households are likely to be included in the eventual sample of opinion? Excluded? d) Suppose, instead, that we continue calling each number, perhaps in the morning or evening, until an adult is contacted and interviewed. How does this improve the sampling design? e) Random-digit dialing machines can generate the phone calls for us. How would this improve our design? Is anyone still excluded?
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