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In carrying out a study of views on capital punishment, a student asked a question two ways: 1\. With persuasion: "My brother has been accused of murder and he is innocent. If he is found guilty, he might suffer capital punishment. Now do you support or oppose capital punishment?" 2\. Without persuasion: "Do you support or oppose capital punishment?" Here is a breakdown of her actual data. $$ \begin{aligned} &\text { Men }\\\ &\begin{array}{lcc} & \begin{array}{c} \text { With } \\ \text { persuasion } \end{array} & \begin{array}{c} \text { No } \\ \text { persuasion } \end{array} \\ \hline \text { For capital punishment } & 6 & 13 \\ \hline \text { Against capital punishment } & 9 & 2 \\ \text { Women } \end{array}\\\ &\begin{array}{lcc} & \begin{array}{c} \text { With } \\ \text { persuasion } \end{array} & \begin{array}{c} \text { No } \\ \text { persuasion } \end{array} \\ \hline \text { For capital punishment } & 2 & 5 \\ \hline \text { Against capital punishment } & 8 & 5 \end{array} \end{aligned} $$ a. What percentage of those persuaded against it support capital punishment? b. What percentage of those not persuaded against it support capital punishment? c. Compare the percentages in parts a and b. Is this what you expected? Explain.

Step by step solution

01

Compute Total Respondents for each Scenario

Compute the total number of people who were questioned in each scenario (With Persuasion and Without Persuasion) by summing up all the respondents. For men with persuasion this total is \(6 + 9 = 15\). Similarly, for men without persuasion the total is \(13 + 2 = 15\). Following the same process, for women with persuasion the total is \(2 + 8 = 10\), and for women without persuasion the total is \(5+ 5 = 10\).

02

Compute the Percentage of People who Support Capital Punishment

To find the percentage of people who support capital punishment, divide the number of people who are For capital punishment by the total number of people in that category and multiply by 100. For men with persuasion, the percentage is \(\frac{6}{15} × 100 = 40%\). For men without persuasion, the percentage is \(\frac{13}{15} × 100 = 86.67%\). For women with persuasion, the percentage is \(\frac{2}{10} × 100 = 20%\). For women without persuasion, the percentage is \(\frac{5}{10} × 100 = 50% \).

03

Compare the Percentages

The percentage of both Men and Women who support capital punishment is lower when they are subjected to persuasion as compared to no persuasion. This indicates that the persuasive method used might be effective in influencing viewpoints.

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Key Concepts

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

Calculation of Percentages

The process of calculating percentages is essential in understanding how different groups respond in a given scenario. Percentages help us to compare proportions in a way that is easy to understand and can reveal trends that raw numbers may not show.

To calculate a percentage, you need to divide the number of individuals who meet a certain criterion by the total number of individuals being considered and then multiply the result by 100. This turns the fraction into a percentage, which is a common way to express ratios.

For instance, if you want to find out what percentage of men supported capital punishment when persuasion was used, you would take the number who supported it (which is 6) and divide it by the total number of men in that group (15). The formula would look like this:

• Percentage supporting = \( \frac{6}{15} \times 100 = 40\% \)

Similarly, by applying this method across different groups and circumstances, we can align the responses in terms of one universal comparison, simplifying the analysis of the survey results.

Persuasion Effects

Persuasion plays a significant role in how individuals form opinions and make decisions. In a survey, the phrasing of questions can drastically influence respondents' answers. This is known as the "persuasion effect."

• A question presented with a persuasive context, like the one involving the notion of an innocent brother facing dire consequences, appeals to the emotions of the respondent.
  It aims to trigger emotional reasoning which might divert the respondents from their initial stand.
• On the other hand, a neutral question devoid of emotional cues invites respondents to rely on their prior beliefs without immediate external influence.

In this study, the persuasive question resulted in a lower percentage of both men and women supporting capital punishment compared to when there was no persuasion. This suggests that persuasive approaches can effectively alter public sentiment, at least momentarily, by evoking empathy or personal reflection.

Data Interpretation

Data interpretation is the process of making sense of numerical data. It involves analyzing the results to uncover patterns, trends, or insights that can inform future decisions or actions.

While interpreting survey data, it is important to look beyond the surface numbers. For instance, in this study:

• The effectiveness of persuasion is evident as the percentage of support for capital punishment drops when emotional context is introduced.
• For men, support decreased from 86.67% to 40% when persuasion was used, exemplifying a substantial persuasion effect.
• For women, the drop was from 50% to 20%, showing a similar trend.

When comparing these results, we observe how powerful the impact of question framing can be, highlighting how interpretation is crucial. It helps derive meaningful conclusions from the data, directing attention to the power of question phrasing in surveys and its potential to influence public opinion.