A survey of 600 people showed that the ratio of those who...

A survey of 600 people showed that the ratio of those who favored candidate $A$ to those who favored candidate $B$ was 7 to $5 .$ Of $24,000$ actual votes cast, candidate A received 13,187. Was this more or less than the number of votes expected for candidate $A$ on the basis of the survey?

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Key Concepts

Ratios

Ratios express the relative sizes of two or more quantities. In problems like this, the ratio is used to compare the number of people favoring one candidate over another, providing a basis to determine expected outcomes based on relative proportions.

Proportional Reasoning

Proportional reasoning involves using the known ratio of quantities to predict other related amounts. It allows one to extend the findings from a smaller sample, such as a survey, to a larger group, such as the overall voter base.

Survey Sampling

Survey sampling is the process of collecting data from a subset of a population to make inferences about the entire population. This concept is crucial when evaluating whether actual outcomes align with survey predictions based on the sample.

Expected Value Calculation

Expected value calculation in this context involves applying the survey's ratio to the total number of votes to predict the outcome. This calculation provides a benchmark that can be compared to the actual votes to assess whether the result deviates from the survey's predictions.

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