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A survey was done of men's and women's hands to see if the ring finger appeared longer than the index finger or not. Yes means the ring finger is longer, and No means the ring finger appears shorter or the same length as the index finger. The students in this survey were told the theory that men are more likely to have a longer ring finger than women because of additional testosterone. \begin{tabular}{|c|c|c|} \hline & Men & Women \\ \hline Yes & 23 & 13 \\ \hline No & 4 & 14 \\ \hline \end{tabular} a. What percentage of the men said No? b. What percentage of the women said No? c. What percentage of the people who said No were men? d. If a large group of 600 men had the same rate of responses as the men in this sample, how many men of the 600 would say No?

Step by step solution

01

Calculate percentage of the men who said No

To calculate the percentage of the men who responded with 'No', take the number of men who said 'No' and divide it by the total number of men, then multiply the result by 100. In this case, we have 4 men who said 'No' and a total of 27 men. So, the calculation would be \((4 / 27) * 100\).

02

Calculate percentage of the women who said No

Similarly, to calculate the percentage of the women who said 'No', take the number of women who said 'No' and divide it by the total number of women, and multiply the result by 100. Thus, we have 14 women who said 'No' out of a total 27 women. So, the calculation would be \((14 / 27) * 100\).

03

Calculate percentage of the people who said No and were men

For part (c), we need to calculate what percentage of the people who said 'No' were men. Thus, we take the number of men who said 'No' and divide it by the total number of people who said 'No', then multiply the result by 100. That gives us \((4 / (14 + 4)) * 100\).

04

Predict for a larger group

In case of part (d), we have the hypothetical situation where a larger group of 600 men had the same rate of responses like the sample. To find how many of them would say 'No', we'd multiply 600 by the percentage of men who answered 'No' in this sample, but remember that the percentage should be in decimal form, meaning divide aforementioned percentage by 100. Thus, we get \(600 * (4 / 27)\).

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Key Concepts

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

Probability Calculation

In probability calculation, each event is assigned a likelihood or probability of occurring. Probability helps us understand how likely an event is, based on past data or inherent randomness. In the context of the survey, probabilities guide us in predicting how many out of a larger group might say 'No', based on the sample we have. In Step 4 of the solution, we take a hypothetical group of 600 men and predict how many might say 'No' by using the existing probability of 4 out of 27 men who said 'No' in the survey. To calculate this, we convert the percentage into a decimal by dividing by 100 and then multiply by the larger group size:

• Calculate probability from sample: \(\frac{4}{27}\)
• Apply to larger group: \(600 \times \left( \frac{4}{27} \right)\)

This shows us how probability can help make predictions or informed estimates about groups different from our initial sample.

Survey Analysis

Survey analysis is crucial to understanding trends and behaviors of certain groups of people through gathered data. In a survey, respondents provide their inputs, which are then analyzed to derive meaningful insights. In this exercise, we use survey data to analyze differences between men and women regarding the length of their ring fingers relative to their index fingers. Such survey analysis involves:

• Collecting responses (Yes/No to ring finger length in this case)
• Grouping data by categories (Men/Women)
• Interpreting the implications of these groups

By comparing the responses, we can analyze trends that could indicate biological differences influenced by factors such as testosterone levels as suggested in the provided theory.

Percentage Calculation

Percentage calculation is a way to express a number as a fraction of 100, which makes it easier to compare and interpret data. In this exercise, percentages are calculated to understand the distribution of 'Yes' or 'No' answers amongst men and women. For example, to find what percentage of men said 'No':

• Identify the number of men who said 'No' (which is 4).
• Total number of men surveyed is 27.
• The calculation becomes: \(\left( \frac{4}{27} \right) \times 100 \approx 14.81\%\).

This calculation allows us to quickly and clearly understand how prevalent the 'No' response is within the subgroup of men.

Data Interpretation

Data interpretation involves making sense of raw data by analyzing and representing it in a form that provides insights. Through data interpretation, we translate data into meaningful information that can support decision-making or hypothesis testing.In the given exercise, data interpretation helps to address questions like:

• How do male and female responses compare?
• What percentage of people saying 'No' are men?

For example, a comparison of 'No' responses can show gender-based differences:

• Calculate the male proportion of 'No' responses: \(\left( \frac{4}{18} \right) \times 100 \approx 22.22\%\)

By interpreting this data, we can understand broader trends or patterns, such as the theory that testosterone affects finger length differences.