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91Ó°ÊÓ

State whether or not the sampling method described produces a random sample from the given population. Send an email to a random sample of students at a university asking them to reply to the question: "Do you think this university should fund an ultimate frisbee team?" A small number of students reply. Use the replies to estimate the proportion of all students at the university who support this use of funds.

Short Answer

Expert verified
The sampling method described does not produce a random sample from the given population because it ends up being a voluntary-response sampling, where respondents themselves decide to respond to the survey, hence introducing a potential bias in the sample.

Step by step solution

01

Checking method of email sending

First, let's consider how the email was sent to a 'random' sample of students. If students were selected randomly and every student at the university had equal chances of getting selected, then the sample of students who received the email can be considered random.
02

Analyze Response Rate

Second, let's look into the response rate. Regardless of the initial selection being random, all initial recipients of the survey may not respond. It becomes a self-selected sample. Not everyone has an equal chance to be included in the final sample because it relies on the individual's initiative.
03

Final Evaluation of Randomness

In conclusion, although the initial email was sent to a random sample of students, the final sample was not random because it was based on the students who responded. Thus, bias may be introduced due to the self-selection of respondents. This final sample may not be representative of the entire university's population, hence, it does not constitute a random sample.

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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 a crucial aspect of research design focused on how survey data is collected and analyzed. It involves techniques to ensure that the responses accurately reflect the group you want to study. In the context of the original exercise, sending emails to students is a part of the survey methodology.
The goal is to gather data that accurately represents the student body's opinion on funding an ultimate frisbee team.

Key elements of survey methodology include:
  • Sampling Design: How the participants are chosen from the larger population.
  • Data Collection Methods: Ways to collect responses, such as emails or interviews.
  • Questionnaire Design: Ensures questions are clearly formulated, unbiased, and easily understood.
A strong survey methodology aims to minimize errors and biases to reflect true opinions. In practice, it balances between being efficient and being rigorous enough to provide valid results.
Response Bias
Response bias occurs when the answers provided by respondents do not reflect their true thoughts or feelings. This can skew the results, making the survey data unreliable for drawing conclusions. In the original exercise, response bias can occur if some students feel pressured to answer in a socially desirable way or if the phrasing of the question leads them to answer in a particular manner.

Several common types of response bias include:
  • Acquiescence Bias: Tendency to agree with statements regardless of content.
  • Social Desirability Bias: Answering in a way deemed favorable by others rather than truthfully.
  • Leading Questions: Questions that suggest a particular answer.
To minimize response bias, ensure questions are neutrally worded and encourage honest responses without fear of judgment. Additionally, anonymity in responses can help reduce social desirability bias by making respondents feel more comfortable in sharing their true opinions.
Sampling Bias
Sampling bias occurs when some members of the intended population are less likely to be included in the survey, leading to a non-representative sample. In the original exercise, even though the initial group receiving the email was random, there is potential for bias since only those who choose to respond are included in the final sample. Thus, the views collected may not reflect the entire population's perspectives.

Here are some causes of sampling bias:
  • Selection Bias: When specific participants are more likely to be chosen due to the sampling process.
  • Non-response Bias: Occurs when respondents who participate differ significantly from those who do not.
  • Voluntary Response Bias: When individuals with strong opinions are more likely to participate.
To mitigate sampling bias, it is essential to ensure all individuals in the population have an equal chance of being selected and encourage high response rates. Another approach is to employ follow-ups or incentives to gather responses from those who may otherwise not participate.

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