# Analyzing the Correlation Between First and Family Names: A Statistical Study

In our comprehensive study, we investigated the potential link between the number of letters in students' first names and their family names. We collected data from ten students, measuring the respective counts of letters in both their first and last names. The statistical analysis aimed to determine if a significant difference existed between the lengths of first and family names. Our findings, which were tested at a 95% confidence level, revealed that there was no substantial difference. However, a visually striking scatter plot showcased a positive relationship between the two, offering valuable insights into this intriguing aspect of personal nomenclature.

## Problem Description

In this correlation analysis assignment, we conducted a study to explore the relationship between the number of letters in students' first names and the number of letters in their family names. To do this, we collected data from ten fellow students and recorded the respective counts of letters in both their first and last names.

## Assignment Solution: Analyzing the Relationship Between First and Family Names

• Hypothesis Testing: We formulated the following null and alternative hypotheses to test this relationship at a significance level of α=0.05:
• H0 (Null Hypothesis): The number of letters in the first name is not more than the number of letters in the family name of individuals. H1 (Alternative Hypothesis): The number of letters in the first name is more than the number of letters in the family name of individuals.

Mathematically, this can be represented as:

• H0: μ_1 - μ_2 = 0
• H1: μ_1 - μ_2 ≠ 0

Here, μ_1 represents the mean number of letters in first names, and μ_2 represents the mean number of letters in family names.

• Calculations: We conducted statistical analyses to test the hypotheses. The results are as follows:

Results: Based on the computed values at a 95% confidence level, we found that we failed to reject the null hypothesis. Therefore, we conclude that the number of letters in the first names of individuals is not significantly more than the number of letters in their family names.

Fig 1: A scatter plot of number of letters in the first and family name

Note: This figure presents a scatterplot illustrating the relationship between the number of letters in the first name and the family name of an individual.

Additionally, from the scatter plot generated from the data, we observed a positive relationship between the number of letters in the first name and the number of letters in the family name of individuals. This visual representation supports our conclusion.

Data: Here is the dataset used for the analysis:

First Name Family Name
6 5
3 8
5 7
7 7
3 5
9 7
6 6
7 6
6 6
5 8