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Emoticons The website www.gamefaqs.com asked, as their question of the day to which visitors to the site were invited to respond, "Do you ever use emoticons when you type online?" Of the 87,262 respondents, \(27 \%\) said that they did not use emoticons.;- a) What kind of sample was this? b) How much confidence would you place in using \(27 \%\) as an estimate of the fraction of people who use emoticons?

Short Answer

Expert verified
The sample was voluntary response, leading to low confidence in the 27% estimate.

Step by step solution

01

Identify Sample Type

The survey conducted by www.gamefaqs.com asks respondents a question when they visit the site. This method of collecting responses is known as a **voluntary response sample** because participants self-select to provide a response to the survey question.
02

Analyze Sample Bias

A voluntary response sample often leads to a biased sample. This means that the individuals who choose to respond may have stronger opinions or interests in the topic, compared to those who do not participate, thus affecting the representativeness of the sample.
03

Assessing Confidence in the Estimate

Given that the sample is based on voluntary responses, there may be significant **bias**. People who chose to respond might have different emoticon usage habits than the general population. Therefore, we should have **low confidence** in the representativeness of the 27% figure to the broader population.

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Key Concepts

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

Sample Bias
Sample bias occurs when the method of collecting samples causes certain groups to be overrepresented or underrepresented in the data. In a voluntary response sample, like the one used by www.gamefaqs.com, bias is a common issue.

This is because only individuals who have a strong opinion or interest in the topic may choose to respond. For instance, people who regularly use emoticons might be more inclined to participate because they find the topic relevant to their interests. Conversely, those who don't might opt-out, thus leading to an underrepresentation of that group.

Sample bias can severely distort the data, leading to conclusions that do not accurately reflect the reality of the broader population. To mitigate sample bias, it is important to use random sampling methods that give all members of the population an equal chance to be selected.
Confidence in Estimates
Confidence in estimates refers to how sure we can be that our sample statistic accurately reflects the population parameter. In the case of the gamefaqs.com survey, confidence is low.

Since the data comes from a voluntary response sample, there's a high likelihood of sample bias. This makes the 27% figure suspicious as a reliable estimate of all people who use emoticons. It likely represents the views of people more passionate about emoticons, thus skewing the results.

Ideally, for high confidence, we would use a method where each member of the population has an equal chance of selection, reducing bias and making the sample more representative. Confidence can be mathematically expressed by confidence intervals, which provide a range within which the true population parameter likely falls. In biased samples, however, these intervals might be inaccurate.
Survey Methodology
Survey methodology is the overarching plan or strategy used to conduct surveys and gather data. It includes the mode of survey (online, phone, in-person), question design, sampling method, and data analysis techniques.

In the case of www.gamefaqs.com, the survey used an online platform and employed a voluntary response sampling method. While convenient, this method has limitations, mainly leading to sample bias, which can reduce the accuracy of inferences made from the data.

Improving survey methodology might involve employing randomized sampling techniques to gather more representative data. Furthermore, question design should be clear and unbiased, ensuring that respondents' answers truthfully reflect their opinions or behaviors. These elements are fundamental to gaining reliable insights from survey data.

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