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Chapter 10: Problem 63

Suppose you are interested in whether more than \(50 \%\) of voters in California support a proposition (Prop X). After the vote. you find the total number that support it and the total number that oppose it.

Short Answer

Expert verified
The exercise can be solved by calculating the total number of voters, finding the proportion of voters who support Prop X and then comparing that with 50%. If the calculated percentage is more than 50%, then more than half of the voters in California support Prop X.

Step by step solution

01

Identify the numbers

First, identify the values from the problem. The total number of people who voted for Prop X and the total number of voters who voted against it.
02

Calculate total voters

Add the number of people who voted for Prop X and the number of people who voted against it. This gives the total number of voters.
03

Find the proportion

Next, divide the number of people who voted for Prop X by the total number of voters to find the proportion of voters who support Prop X.
04

Convert to percentage

To convert the proportion to a percentage, multiply it by 100.
05

Compare with 50%

Finally, compare the percentage of voters who support Prop X with 50%. If it is more than 50%, then more than half of the voters support Prop X.

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Key Concepts

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

Proportion Calculation
Proportion calculation is a crucial concept to understand when approaching questions related to parts of a whole. In the context of our voting example, to find out what proportion of voters support Prop X, we start by identifying the required numbers: the number of people who voted for the proposition (let's call this number \( V_f \)) and the total number of voters (\( V_t \)).
Once you have these numbers, calculating the proportion is straightforward. Just divide the number of favorable votes \( V_f \) by the total number of votes \( V_t \), as shown in the formula: \[ P = \frac{V_f}{V_t} \] This result, \( P \), gives you the proportion of people who supported the proposition in its fractional form.
This step is fundamental because it provides a clear measure of support from the group, differing from raw numbers.
Percentage Conversion
Once you have the proportion of voters supporting the proposition, converting this into a percentage makes it easier to interpret and communicate to others. A percentage expresses the same value as a part of 100, making it a universally understood format. To convert the proportion \( P \) into a percentage, multiply the proportion by 100.
The conversion is achieved with the formula: \[ ext{Percentage} = P \times 100 \] Let鈥檚 say, hypothetically, the proportion of people supporting Prop X is 0.56. Thus, the corresponding percentage would be 56%. This helps us more intuitively compare parts of a whole, whether they meet, exceed, or fall short of a benchmark.
Converting to percentage is especially useful when you need to answer specific questions; for example, in this case, whether support exceeds a certain threshold, typically 50%.
Data Analysis
Data analysis in this context involves interpreting the calculated values to derive meaningful conclusions. After converting the proportion to a percentage, the next step is analytical - comparing this percentage with a reference point. Here, that point is 50%.
Through this comparison, we determine if the voters' support for Prop X is significant or not. If the percentage is greater than 50%, it indicates a majority support for the proposition, suggesting strong acceptance among voters.
Data analysis is not just about processing numbers; it all comes down to what these numbers tell us about real-world phenomena. Reliable data analysis considers accuracy and ensures that any conclusions drawn are supported by the calculations.
Understanding this concept helps in making data-driven decisions, whether in policy-making, business, or personal contexts.

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Most popular questions from this chapter

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