Problem 31 - Algebra 2

Question

a. Elections A poll of 150 voters shows that a candidate is preferred by 5\(\%\) of the voters while 44\(\%\) prefer the opponent. Should the candidate be concerned? Explain. b. A later poll of 600 voters shows the candidate is preferred by 55\(\%\) of the voters. Should this candidate feel more or less confident, given the results of the second poll? Explain.

Step-by-Step Solution

Answer

The candidate, initially preferred by around 8 voters out of 150 and significantly less popular than the opponent, should have been concerned. However, the second poll shows a substantial increase in both support percent and total supporters (330 out of 600). So the candidate should now feel more confident.

Step 1: Interpret the first poll

In the first poll, which consists of 150 voters, the candidate is preferred by 5\(\%\) of the voters. 5\(\%\) out of 150 voters equals 7.5 voters, but you can't have half a voter, so round up to 8. Thus, this candidate is preferred by roughly 8 voters out of 150. The opposing candidate has the preference of 44\(\%\) of voters, which equals 66 voters out of 150.

Step 2: Analyse the candidate's situation

From the first poll, it's clear that the candidate has significantly less support than the opponent, with roughly only 8 compared to 66. Therefore, the candidate should indeed be concerned.

Step 3: Compare the results of the second poll

In a later poll of 600 voters, the candidate is preferred by 55\(\%\) of the population. 55\(\%\) out of 600 equals 330 voters. This is an increase in both percentage and total number of supporters.

Step 4: Analyse the second poll's implications

With the new poll showing that the candidate is preferred by 330 people, compared to the initial 8 (or estimated 7.5), this candidate should feel more confident given the results of the second poll.

Key Concepts

Poll Interpretation

When participating in elections, understanding how to interpret polling results is crucial. Poll interpretation involves analyzing the data collected to make informed decisions or predictions about the outcome of an election. Consider the two polls conducted in our exercise.
In the first poll, 150 voters were asked whom they prefer for a certain position. The candidate was favored by only 5\(\%\), which translates to approximately 8 people once we round up. Meanwhile, the opponent was preferred by 44\(\%\), approximately 66 voters.
Recognizing these numbers, one can identify that the candidate has significantly less support. To effectively interpret polls, think of them as a snapshot that shows current voter preferences.

• Check the percentage of response for each option.
• Convert the percentages into actual numbers to grasp the magnitude of support.

This process gives a clear picture of where a candidate stands at a given moment.

Voter Analysis

Voter analysis is the process of extracting meaningful insights from poll data. It involves comparing different polling results to understand trends and shifts in voter behavior. In our example, let's analyze the candidate's situation based on the two polls.
The first poll indicates low support for the candidate in contrast with the opponent's strong preference among 150 voters. This tells us that, at that time, the candidate would need to step up their campaign efforts significantly.
However, in a subsequent poll consisting of 600 voters, the candidate receives support from 55\(\%\). This translates to 330 voters, showing a substantial increase in their backing. Understanding these numbers helps relate how campaign changes and external factors influence voter support.

• Look for patterns and changes across polls.
• Assess potential reasons for shifts in voter preferences like changes in campaign strategy or significant events.

This analysis helps strategize future actions for more effective campaigning.

Percentage Calculation

Knowing how to calculate percentages is essential for interpreting poll data. Calculating percentages allows candidates and analysts to quantify voter support. Let’s break down the calculations from our exercise.
To determine how many voters prefer each candidate based on percentages, follow these steps:

• Multiply the total number of surveyed voters by the percentage expressed as a decimal. For example, 5\(\%\) of 150 voters: 150 \(\times\) 0.05 \(= 7.5\), then round to 8.
• Repeat this calculation for the preferred percentage of the opponent or any additional candidates.

In the second poll, when assessing 600 voters with 55\(\%\) preference:

• Calculate 600 \(\times\) 0.55 to equal 330 voters preferring the candidate.

Percentage calculations provide a measurable way of comparing and contrasting voter preferences between different polls, allowing for precise planning and decision-making.