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# Assessing Proportions of SchoolSES Categories and Independence between Gender and SchoolSES

In this assignment, we delve into the examination of the proportions of SchoolSES categories (High, Low, Medium) and explore the potential independence between Gender and SchoolSES. Through statistical tests, we aim to understand the distribution of SchoolSES categories and whether Gender plays a role in determining SchoolSES.

## Problem Description:

In this statistical assignment, the focus is on understanding the distribution of SchoolSES categories (High, Low, Medium) and investigating the potential relationship between Gender and SchoolSES. The objective is to employ rigorous statistical analyses, including chi-squared tests, to assess whether the proportions of SchoolSES categories are equal and if there exists an association between Gender and SchoolSES. By delving into these aspects, the assignment aims to provide valuable insights into the distribution of socioeconomic status among students and whether this distribution is influenced by gender.

## Testing Proportions of SchoolSES Categories

State the Hypotheses

• Null Hypothesis (H₀): The proportions of each of the three categories of SchoolSES (High, Low, Medium) are equal.
• Alternative Hypothesis (Hₐ): The proportions of at least one of the SchoolSES categories are different from the others.

Set the Significance Level

• α = 0.05

Perform the Test and Analyze Results

Chi-squared test for given probabilities

data: SchoolSES

X-squared = 19, df = 2, p-value = 7.485e-05

Expected frequencies

High                Low             Medium

66.66667        66.66667      66.66667

The chi-squared test reveals a significant relationship (χ²(2) = 19, p < 0.001). As the p-value is less than the significance level, we reject the null hypothesis, suggesting that the proportions of SchoolSES categories are not equal.

Testing Independence between Gender and SchoolSES

State the Hypotheses

• Null Hypothesis (H₀): There is no association between Gender and SchoolSES.
• Alternative Hypothesis (Hₐ): There is an association between Gender and SchoolSES.

Set the Significance Level

• α = 0.05

Perform the Test and Analyze Results

Pearson's Chi-squared test

data: contingency_table

X-squared = 0.25819, df = 2, p-value = 0.8789

Expected frequencies

High      Low      Medium

Female      20.8        46.8          36.4

Male           19.2       43.2           33.6

The test does not find a significant association (χ²(2) = 0.25819, p = 0.8789). As the p-value is greater than the significance level, we fail to reject the null hypothesis, indicating no significant relationship between Gender and SchoolSES.

APA Write-up

A chi-squared test was conducted to examine whether the proportions of the three categories of SchoolSES (High, Low, Medium) are equal. The test revealed a significant relationship between SchoolSES categories (χ²(2) = 19, p < 0.001). Thus, we reject the null hypothesis, indicating that the proportions of SchoolSES categories are not equal.

A Pearson's chi-squared test was performed to assess the relationship between Gender and SchoolSES. The test did not find a significant association between Gender and SchoolSES (χ²(2) = 0.25819, p = 0.8789). Therefore, we fail to reject the null hypothesis, suggesting that there is no significant relationship between Gender and SchoolSES.

In both analyses, the assumptions related to expected cell frequencies were met, indicating that the sample sizes were adequate for conducting the chi-squared tests. As a result, we can have confidence in the validity of the chi-squared test results.

## Conclusion

In conclusion, the analyses revealed that the proportions of SchoolSES categories (High, Low, Medium) are not equal. Additionally, there is no significant association between Gender and SchoolSES. These findings suggest that the SchoolSES categories are unevenly distributed, and Gender does not appear to be associated with different SchoolSES categories.