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Chapter 10: Problem 29

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

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The biases in this survey sample include a self-selection bias, because only those who visit the park are giving input, and a voluntary response bias, as these parents might have particularly strong opinions about the playground. These biases could be minimized by including residents who do not visit the park regularly and implementing random sampling.

Step by step solution

01

Identify the sampling method

The first step is to understand the sampling method used for the survey. Here the questionnaires are handed out to parents who bring their children to the park.
02

Look for potential biases

Next, analyze the sampling method to determine if there are potential biases. Since the survey is taken from parents who are bringing their children to the park, there are two notable biases. The first bias is the self-selection bias, where only those who visit the park are included in the survey, excluding the opinion of those who do not visit the park. The second bias is the voluntary response bias, as those parents may already have a strong opinion, either positive or negative, about the playground.
03

Offer solution to minimize biases

To reduce these biases, it would be beneficial to extend the sampling method to include residents who do not visit the park regularly or at all, and to use random sampling. This can be done by mailing questionnaires to random households in the city or conducting phone surveys.

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Key Concepts

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

Self-Selection Bias
When surveying opinions on a community project, like the renovation of a playground, ensuring a representative sample is crucial for accurate results. Self-selection bias occurs when individuals have the opportunity to choose whether to participate, often leading to a skewed sample that doesn't reflect the broader population's views.

In the park managers' survey, this bias is clear: only parents who visit and thus have an interest in the playground are surveyed. Their responses might not match the opinions of all city residents. Parents too busy to visit or without children may hold different views on the importance or necessity of repairs. To limit self-selection bias, consider alternative strategies like distributing questionnaires across a variety of public spaces or using digital platforms to reach a broader audience.
Voluntary Response Bias
Voluntary response bias is another concern in survey data collection. This type of bias arises when participants who feel strongly about an issue are more likely to respond. In the playground example, those parents with strong positive or negative feelings about the park's condition are more likely to fill out questionnaires.

Their passion can lead to overrepresentation of extreme perspectives, which might misinform park managers about the average resident's viewpoint. To mitigate this, unbiased methods such as random-digit dialing for phone surveys or online surveys with controlled invitations can ensure more moderate and diverse opinions are captured.
Random Sampling
Random sampling is a gold-standard method for gathering data that is representative of a whole population. It mitigates the issues posed by both self-selection and voluntary response biases. By randomly selecting individuals to participate, every member of the population has an equal chance of being included, which enhances the diversity and accuracy of responses.

For the playground survey, park managers could utilize random sampling by using a citywide registry to randomly select residents to contact. This might involve mailing surveys to these randomly chosen addresses or calling a random selection of phone numbers. Conducting the survey in this manner would provide a clearer, more accurate sense of the general public's opinion regarding the playground's future.

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Most popular questions from this chapter

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 \(21 ?\)

Fuel economy Occasionally, when I fill my car with gas, 1 figure out how many miles per gallon my car got. I wrote down those results after six 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?

Roper Through their Roper Reports Worldwide, GfK Roper conducts a global consumer survey to help multinational companies understand different consumer attitudes throughout the world. Within 30 countries, the researchers interview 1000 people aged 13-65. Their samples are designed so that they get 500 males and 500 females in each country. (www.gfkamerica.com) a. Are they using a simple random sample? Explain. b. What kind of design do you think they are using?

Sampling students A professor teaching a large lecture class of 350 students samples her class by rolling a die. Then, starting with the row number on the die (1 to 6 ), she passes out a survey to every fourth row of the large lecture hall. She says that this is a simple random sample because everyone had an equal opportunity to sit in any seat and because she randomized the choice of rows. What do you think? Be specific.

In Exercises 17 ? to 23 ?, for the reports about statistical studies, identify the following items (if possible). If you can't tell, then say so - this often happens when we read about a survey. a. The population b. The population parameter of interest c. The sampling frame d. The sample e. The sampling method, including whether or not randomization was employed f. Who (if anyone) was left out of the study g. Any potential sources of bias you can detect and any problems you see in generalizing to the population of interest Mayoral race Hoping to learn what issues may resonate with voters in the coming election, the campaign director for a mayoral candidate selects one block from each of the city's election districts. Staff members go there and interview all the adult residents they can find.
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