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Question

Difficulty: MediumStatistical Sampling and Studies

A researcher wants to estimate the proportion of registered voters in a county who support a proposed sales tax increase. The county has 50,00050,000 registered voters. The researcher randomly selects 400400 registered voters from a list of those who voted in the most recent school board election. Of the selected voters, 60%60\% support the proposed tax increase. Which of the following is the most appropriate conclusion?

  1. A
    The proportion of all registered voters in the county who support the proposed sales tax increase is approximately 60%60\%.
  2. The proportion of registered voters in the county who voted in the most recent school board election who support the proposed sales tax increase is approximately 60%60\%.Answer
  3. C
    The proportion of all residents in the county who support the proposed sales tax increase is approximately 60%60\%.
  4. D
    Exactly 240240 registered voters in the entire county support the proposed sales tax increase.

Answer

The proportion of registered voters in the county who voted in the most recent school board election who support the proposed sales tax increase is approximately 60%60\%.
The correct conclusion must limit its generalization to the population from which the sample was randomly selected. Because the researcher selected the sample from a list of voters in the school board election, the findings can only be generalized to that specific subpopulation of voters. Therefore, we can estimate that approximately 60%60\% of school board election voters in the county support the sales tax increase.

Step-by-Step Solution

1
Identify the population from which the random sample was selected.
The sample of 400400 registered voters was randomly selected from the subpopulation of voters who participated in the most recent school board election.
Generalization of survey results is limited to the population from which the random sample was selected.
2
Determine the appropriate population for generalization.
The results can be generalized to estimate the proportion of registered voters who voted in the school board election who support the tax increase, which is approximately 60%60\%.
Since the sample was not randomly selected from all registered voters or all residents of the county, it cannot be generalized to those broader groups due to potential selection bias.

Key Concept

Statistical Generalization and Selection Bias
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Topics

Statistical Sampling and Studies

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