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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鈥檚 management to conduct a survey at the stadium, but they will not allow you to bother the fans in the club seating or box seats (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. (a) Provide a reason why this survey might yield a biased result. (b) Explain whether the reason you provided in (a) is a sampling error or a non sampling error.

Short Answer

Expert verified
The survey is biased because it excludes those with potentially higher spending. This is a sampling error.

Step by step solution

01

Identify Potential Bias in the Sampling Method

The survey excludes fans in club seating or box seats, who typically spend more on tickets and possibly related expenses like food and merchandise. By not including these individuals, the survey might not reflect the true average spending of all fans attending the game.
02

Determine the Type of Error

The bias identified arises because certain groups of people (those in more expensive seats) are systematically omitted from the sample. This leads to an underestimation of average spending by fans since a significant segment with likely higher spending power is excluded. As this issue pertains to the sample being non-representative of the whole population, it constitutes a sampling error.

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Key Concepts

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

Survey Design
When designing a survey, it's essential to carefully consider which groups should be included to ensure the data gathered accurately reflects the target population. In this baseball game scenario, the survey design restricted data collection to certain seating areas and excluded club and box seat holders. This introduced bias, as these fans likely have different spending patterns compared to others.
Survey design involves:
  • Defining the purpose: The goal in our example is to determine the average amount fans spend.
  • Identifying the target population: All fans attending the game, but certain fans were excluded.
  • Selecting a sampling method: Randomly selecting seats can be effective, but not if significant groups are left out.
  • Determining how data will be collected: In-person surveys during a game might cause distractions, influencing the quality of responses.
Surveys should be as inclusive as possible, or they risk overlooking crucial data, which can skew results. Consideration of all potential variables that might affect responses ensures a more representative and accurate outcome.
Sampling Error
Sampling error occurs when a selected sample does not adequately represent the population. This can lead to incorrect conclusions about the entire group. In this exercise, the sampling error arose because the survey excluded a segment of fans who were likely significant contributors to average spending.

Common sources of sampling error include:
  • Sample selection bias: Omitting certain groups can misrepresent the population.
  • Sample size: A small sample may not capture the diversity of the population.
  • Random variation: Sometimes, despite random selection, a sample may not reflect real-world distributions.
To minimize sampling error, ensure samples are drawn randomly and representatively. The more inclusive a sample is, the closer its data will be to the true characteristics of the entire population. In our example, including all seating categories would likely mitigate the error, providing a truer reflection of spending habits.
Data Collection Methods
Data collection methods are the strategies used to gather information from respondents. In the context of surveying fan spending at a baseball game, the method chosen greatly affects the reliability and validity of the data.

Key elements of data collection include:
  • Selection of respondents: Ideally, fans should be chosen in a way that captures diverse spending behaviors.
  • Questionnaire design: Questions should be clear and concise to gather accurate data.
  • Mode of data collection: In-person, digital, and paper surveys each have their pros and cons. In-person surveys might disrupt fan engagement during a game.
  • Timing: Conducting surveys during different stages of a game might influence spending reports. Fans might report different expenditures pre-game compared to mid- or post-game.
By carefully designing data collection methods, researchers can ensure they capture comprehensive data that accurately reflects the sample's behaviors and characteristics, leading to more reliable insights. In our example, expanding methods beyond the restricted seating areas or using multiple methods can aid in rectifying survey limitations.

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Most popular questions from this chapter

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