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Chapter 4: Problem 29

Suppose you want to know the average amount of money spent by the fans attending opening day for the Cleveland Indians baseball season. You get permission from the team's management to conduct a survey at the stadium, but they will not allow you to bother the fans in the club seating or box scats (the most expensive seating). Using a computer, you randomly select 500 seats from the rest of the stadium. During the game, you ask the fans in those seats how much they spent that day. Give a reason why this survey might yield a biased result. Explain the likely direction of the bias.

Short Answer

Expert verified
The survey might be biased towards underestimating the average expenditure, as it excludes the highest spending fans.

Step by step solution

01

Understanding the Survey Method

In this survey, you are collecting data from fans who are willing to participate, but you are excluding those in the most expensive seats in the stadium.
02

Identifying Bias Possibilities

The exclusion of fans from club seating and box seats means you are omitting those who might spend more money, as these seats are typically occupied by individuals willing to spend more for a premium experience.
03

Analyzing the Impact of Bias

Because fans in the most expensive seats tend to spend more on concessions and other purchases, excluding them from the survey can lead to an underestimation of the average amount of money spent by fans at the stadium.

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Key Concepts

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

survey methodology
Survey methodology is the framework that guides how surveys are structured, conducted, and analyzed. A well-designed survey can provide valuable insights, but it must be carefully planned to ensure accuracy and reliability.

When crafting a survey, several elements must be considered:
  • **Sampling method**: This includes decisions on how participants are chosen. Random sampling is often used to avoid bias, but it must truly represent the whole population.
  • **Question design**: Questions should be clear and concise to prevent any misunderstanding or leading responses that can skew results.
  • **Administration method**: How the survey is delivered (e.g., online, face-to-face) can affect who responds and the quality of the responses.


In the case of the baseball fans' survey, the methodology involves randomly selecting a sample from available seat holders, excluding club and box seat attendees. This method is partly effective but introduces potential biases by leaving out specific groups.
data collection
Data collection is a vital step in any research process, as it directly influences the study's conclusions. Effective data collection involves organizing and implementing the tools and methods for gathering information.

In this context, data was collected via in-person surveys at a baseball game, which provides firsthand insights but has constraints. Some factors to consider in data collection include:
  • **Access to participants**: Ensuring that all relevant groups are included. Omissions can lead to bias.
  • **Participant willingness**: Not everyone approached may be willing to provide information, affecting sample size and data reliability.
  • **Practical limitations**: Physical restrictions, like being unable to survey certain seating areas, can skew results.


For the Cleveland Indians survey, only those outside the club and box seats were included, potentially leading to an incomplete picture, as it leaves out higher-spending attendees.
bias analysis
Bias analysis in surveys is critical as it helps identify and address factors that might distort findings. Bias can mislead results and obscure the true characteristics of the studied population.

There are several types of bias researchers should look for:
  • **Selection bias**: Occurs when certain groups are systematically excluded or underrepresented, as seen in the exclusion of expensive seat holders in the baseball fans' survey.
  • **Response bias**: Happens during data collection if participants are not answering truthfully or misunderstand questions.
  • **Measurement bias**: Relates to how data is recorded and interpreted, potentially leading to inaccuracies.


For this survey, the likely direction of bias is underestimation. By excluding those sitting in more costly areas, which likely spend more, the average money spent is likely lower than the true figure for all fans attending the game. Recognizing and adjusting for these biases can significantly improve the accuracy of survey results.

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