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Chapter 2: Problem 20

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
The criticism raised by the chairman reflects a misunderstanding of the statistical principles of sampling. The size of a sample is largely contingent on the required accuracy level, not on the population size. A sample of 1000 individuals, randomly selected, can significantly represent the population with a margin of error around 3% to 4%.

Step by step solution

01

Understanding Sampling

In statistics, sampling means selection of observations from a population of interest so that by studying the sample, insights could be drawn about the population. It's not practical to survey entire populations, especially when populations are large, like voters in California. Therefore, the Field poll gathered responses from a random sample of 1000 registered voters.
02

Response to Criticism

The criticism lodged by the chairman misunderstands the basic principles of statistical sampling. The size of the sample depends upon the desired level of accuracy and not on the size of population. A sample of 1000 people is large enough to represent the population and is statistically significant. The sample is randomly selected, which ensures that every individual of the population had an equal chance of being chosen and helps reduce bias.
03

Concept of Margin of Error

While it is true that a larger sample size decreases the margin of error, beyond a certain point, increasing sample size yields diminishing returns. Even if the sample size was increased many times over, it would have only a minor impact on the margin of error. For the poll in question, the margin of error likely would have been about 3% to 4%.

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