Chapter 6: Problem 31
There are about 150 million registered voters in the United States. Pollsters question 2056 of them to get an accurate prediction of an upcoming vote, to a plus or minus \(4 \%\) accuracy. Approximately what percent of the voters is this? A. \(0.0014 \%\) B. \(0.014 \%\) C. \(0.14 \%\) D. \(1.4 \%\)
Short Answer
Step by step solution
Understand the Problem
Set Up the Equation
Perform the Calculation
Simplify the Calculation
Final Calculation and Comparison
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Percentage Calculation
By plugging these numbers into the formula, we can determine the percentage. After simplifying the calculations, we round off the final value to match the given answer choices. This final value tells us the proportion of the total voter population that the sample represents.
Proportion
To do so, we use the percentage formula to transform this proportion into a meaningful number. This helps us gauge how representative the sample size is of the population. It’s useful in many contexts, including surveys and predictions, to ensure that the sample size is adequate for the conclusions being drawn.
Problem-Solving Steps
1. **Understand the Problem**: Identify what is being asked. Here, it’s the percentage representation of the sample size.
2. **Set Up the Equation**: Write down the relevant equation using the percentage formula.
3. **Perform the Calculation**: Substitute the known values into the formula and solve.
4. **Simplify the Calculation**: Break down the math to make it more manageable. Simplify fractions and multiply as needed.
5. **Final Calculation and Comparison**: Calculate the final value and compare it to the provided options to choose the correct answer.
Following these steps systematically helps simplify complex problems and makes finding solutions more manageable.
Voter Statistics
This example highlights how critical it is to choose a representative sample that can accurately reflect the broader population. A sample that's too small may not provide reliable predictions, while a sample that's too large can be unnecessarily costly and time-intensive.
By using mathematical tools like proportion and percentage calculations, statisticians can ensure that they draw well-founded conclusions from their data. Understanding these calculations is essential for interpreting survey results and making informed decisions based on voter statistics.