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Chapter 1: Problem 28

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." This was so dishonest, he added, 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
In response to the chairman's criticism, the proportion of the sample to the population is not as relevant as the sample size itself in determining the accuracy of the survey. The Field poll employs a random selection process and a sample size of 1000 registered voters, which is consistent with standard practices and provides an acceptable margin of error for estimating the opinions of California's registered voters. The main factor in estimation accuracy is the sample size, and a sample size of 1,000 provides a margin of error of about 3%, which is considered acceptable for most surveys.

Step by step solution

01

Understanding the Field Poll and Sampling Method

The Field poll is designed to estimate the opinions of California's registered voters on a specific ballot measure. The sample of 1000 registered voters is randomly selected, meaning that each registered voter has an equal chance of being included in the sample. This approach ensures that the sample is representative of the population, which is a crucial factor in estimating the population's opinion.
02

Calculating the Proportion of Sample to Population

In order to address the chairman's criticism that Field's sample is equivalent to one out of 17,505 voters, let's calculate the proportion of the sample size to the population size. Assuming the population size (number of registered voters in California) is P, and the sample size is 1000, the proportion would be: Proportion = (Sample size) / (Population size) = 1000 / P If P = 17,505,000 (according to the chairman's statement), then: Proportion = 1000 / 17,505,000 鈮� 0.0000571 This indicates that the sample size is slightly more than 0.00571% of the population of registered voters.
03

Importance of Sample Size in Estimation

The important factor in estimating the population's opinion is not the proportion of the sample to the population, but rather the sample size itself. A larger sample size provides a more accurate estimation of the population's opinion with a smaller margin of error. In survey-based research, a common rule of thumb for determining an appropriate sample size is to have at least 1,000 respondents. This is because a sample size of 1,000 has a margin of error of about 3%, which is considered acceptable for most surveys.
04

Responding to the Criticism

To respond to the chairman's criticism, one could argue that the proportion of the sample to the population is not as relevant as the sample size itself in determining the accuracy of the survey. The Field poll, with its random selection process and a sample size of 1000 registered voters, is consistent with standard practices in the survey field and provides an acceptable margin of error for estimating the opinions of California's registered voters. It's essential to understand that polls are never perfect, but by employing a proven sampling method and an appropriate sample size, they can offer valuable insights into the preferences and opinions of a larger population.

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Key Concepts

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

Survey Research
Survey research is a crucial tool for understanding public opinion and making data-driven decisions in various fields, from politics to marketing. In its essence, survey research involves collecting data from a subset of individuals to infer insights about a larger population. This method rests on the foundational principle of taking representative samples.

In the case of the Field poll discussed in the exercise, survey research was employed to gauge the opinions of California's registered voters regarding a ballot initiative. The random sampling method used helps to ensure that each voter has an equal chance of being selected, promoting the accuracy and reliability of the poll's findings. Despite the criticism, the use of a well-constructed survey can provide a snapshot of the electorate's stance, within a known margin of error, without needing to ask every single voter.
Population Representation
The representation of a population in survey research is determined by how well the sample reflects the diverse characteristics of the entire group. The goal is for the chosen sample to be a small-scale representation of the larger population, capturing its variations in opinions, demographics, and other factors.

In our exercise, the critique hinges on the misconception that only proportionate sampling can lead to accurate population representation. However, it's not merely the ratio of the sample to the population that matters; instead, statistical rigor in selecting a random and sufficiently large sample is imperative. Even with a small percentage of the voter population surveyed, a random sample of 1000 responders can adequately represent California voters if the sampling process is unbiased and randomization is properly implemented.
Margin of Error
The margin of error is a statistic that reflects the potential discrepancy between the survey results and the true values for the whole population. It accounts for sampling variability and indicates the level of uncertainty in survey findings. Often expressed as a plus-or-minus figure, this margin is influenced by both the sample size and the population size, although the former plays a more significant role once the sample reaches a certain threshold.

For a typical sample size of 1000 individuals, the margin of error is commonly around 3% for a 95% confidence level. This means there is a 95% probability that the actual opinion of the entire voter population falls within 3% of the survey results, underscoring the reliability of such a sample size for making inferences about the larger group. Responding to criticisms like the one in the exercise, it's important to emphasize this statistical concept to convey that while the sample may represent a tiny fraction of the population, the margin of error provides a quantifiable measure of the result's accuracy.

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Most popular questions from this chapter

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