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In 2000 , the chairman of a California ballot initiative campaign to add "none of the above" to the list of ballot options in all candidate races was quite critical of a Field poll that showed his measure trailing by 10 percentage points. The poll was based on a random sample of 1000 registered voters in California. He is quoted by the Associated Press (January 30, 2000) as saying, "Field's sample in that poll equates to one out of 17,505 voters," and he added that this was so dishonest that Field should get out of the polling business! If you worked on the Field poll, how would you respond to this criticism?

Short Answer

Expert verified
Random sampling ensures that each member of a population has an equal chance of being selected, and the sample size used in the Field poll is a standard number statistically sound for obtaining an accurate representation. The chairman's criticism is a misunderstanding of polling methods and the misinterpretation of the information presented in the polls.

Step by step solution

01

Understanding Random Sampling

Random sampling is a statistical method that ensures that every member within the pool has an equal chance of being selected. This technique does not consider the size of the population (voting base), instead it focuses on how the sample is chosen. The Field Poll was not intending to poll every voter - instead, a random sample of voters was selected.
02

Understanding Sample Size

The sample size of 1000 voters is standard and statistically sound for polling. Despite the total number of voters being around 17 million, a sample size of 1000 is broad enough to get an accurate representation of the opinions or attitudes of the overall population. Larger polls are generally more precise, but the improvement in precision tends to be minimal beyond a certain sample size. In most cases, a sample size of 1000 voters would yield a margin of error of about 3%.
03

Addressing the Chairman's Misinterpretation

The chairman's statement about one out of every 17,505 voters being polled is a misinterpretation of how polling works. In statistical terms, it doesn’t matter if you have a population of 100 people or 10 million people, a well-conducted poll of about 1,000 people can deliver reliable results with a 3% margin of error.

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Key Concepts

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

Sample Size
When conducting a poll, one of the main considerations is determining an appropriate sample size. The sample size refers to the number of individuals selected from the entire population to participate in the survey. For a vast population, such as registered voters in California, employing a sample size of about 1000 is standard practice.
Even if you have millions in the entire content pool, testing a subset of around 1000 helps to maintain statistical reliability. The reason behind this is that 1000 participants can offer a good snapshot of the entire population's views or behaviors. While increasing the sample size generally improves precision, there is a point of diminishing returns where more samples don't significantly change the outcome.
  • Statistical studies suggest that beyond certain sample sizes, increases can result in only minimal gains in accuracy.
  • A 1000-participant poll can often provide a 3% margin of error, which is fairly adequate for understanding public sentiment.
This makes polls practical and cost-effective, saving time and resources while still maintaining accuracy.
Margin of Error
The margin of error is an important concept in statistics, especially in the context of polling or surveys. It measures how much the results might vary from the true population value. When Field Poll reported their results from a sample size of 1000 voters, they claimed a margin of error around 3%. Think of the margin of error as an indicator of predictive accuracy. It tells us that if a poll finds 50% of a sample supports a particular issue, the actual support in the larger population is likely between 47% and 53%.
  • Margin of error decreases when the sample size increases, because a larger sample gives more data and therefore, more accurate estimations.
  • However, even with a 3% margin, a poll result can still give a reliable depiction of public opinion.
  • The smaller the margin of error, the closer your survey responses should reflect the entire population.
Understanding the margin of error helps one interpret poll results with the proper perspective, recognizing the inherent uncertainties of sampling.
Statistical Representation
Statistical representation plays a vital role in interpreting the results of a poll or survey. It involves using a subset of a population to represent the entire population as accurately as possible. In the context of the Field poll in question, a random sample of 1000 voters acts as a proxy for millions of voters in California. The key is ensuring that this smaller sample group genuinely mirrors the demographics and opinions of the broader group. This means the sample should include varied representation across ages, sexes, races, and other important voter segments.
  • Random sampling helps achieve a representative sample by giving each member of the population an equal chance to be chosen.
  • This method reduces biases that might distort the results if certain groups are over or under-represented.
  • A well-chosen random sample can accurately reflect the diverse views of a large number of people.
To make sense of a poll's results, it's crucial to comprehend how statistical representation is achieved and how it strives to deliver accurate data reflective of the wider opinions or characteristics of the entire voting body.

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Most popular questions from this chapter

The article "Tots' TV-Watching May Spur Attention Problems" (San Luis Obispo Tribune, April 5. 2004) describes a study that appeared in the journal Pediatrics. In this study, researchers looked at records of 2500 children who were participating in a long-term health study. They found that \(10 \%\) of these children had attention disorders at age 7 and that hours of television watched at age 1 and age 3 was associated with an increased risk of having an attention disorder at age 7 . a. Is the study described an observational study or an experiment? b. Give an example of a potentially confounding variable that would make it unwise to draw the conclusion that hours of television watched at a young age is the cause of the increased risk of attention disorder.

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Briefly explain why it is advisable to avoid the use of convenience samples.

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