To formulate a research question and null hypothesis related to postgraduate enrollment by program, by gender, and by course, we first need to understand the structure and content of the data available. The preview of the file "Evbogbsi-Edekin-Module 3 plus- Practicals 1.xlsx" suggests it contains enrollment data categorized by program (PGD, Masters, Ph.D.) and gender (Male, Female), along with totals.

Research Question:
What are the patterns of postgraduate enrollment across different programs (PGD, Masters, Ph.D.) with respect to gender?

Null Hypothesis:
There is no significant difference in postgraduate enrollment numbers between genders across different programs (PGD, Masters, Ph.D.).

The data from the first sheet provides enrollment numbers by program (PGD, Masters, Ph.D.), by gender (Male, Female), and by course. To answer the research question and test the hypothesis, we'll perform the following steps:

The analysis of postgraduate enrollment data by program and gender revealed the following key findings:

The visualization suggests varying patterns of enrollment by gender across different programs, indicating potential areas for further investigation and analysis.

To further analyze the data and test the null hypothesis, we'll conduct a chi-square test of independence. This statistical test will help us determine if there's a significant difference in postgraduate enrollment numbers between genders across different programs (PGD, Masters, Ph.D.).

The chi-square test compares the observed frequencies of enrollment by gender in each program to the expected frequencies if there were no association between gender and enrollment in these programs.

Let's proceed with the chi-square test.

The attempt to perform a chi-square test of independence resulted in an unexpected outcome, with the chi-square statistic and p-value being NaN. This suggests there was an issue with the input data provided to the chi-square test function, possibly due to missing or incorrect data formatting.

To address the issue with the chi-square test, we'll first ensure that the data preparation step correctly sums up enrollment numbers by gender for each program type (PGD, Masters, Ph.D.). It's crucial that the data used for the chi-square test is accurate and appropriately structured.

Let's re-examine and correct the data preparation process for the chi-square test.

It appears there was a misstep in aggregating the data for the chi-square test, resulting in NaN values in our contingency table. This issue likely stems from the way we attempted to sum the data, possibly due to incorrect handling of the data types or an error in the aggregation logic.

To correct this and proceed with the chi-square test:

Let's start by verifying and correcting the data format, then accurately summing the enrollment numbers.

The corrected analysis, including the chi-square test, provided the following results:

These results indicate a significant difference in postgraduate enrollment numbers between genders across different programs (PGD, Masters, Ph.D.). The extremely low p-value (2.43e-15) suggests that the observed differences in enrollment numbers are highly unlikely to have occurred by chance, thus leading us to reject the null hypothesis.

Conclusion:
There is a significant difference in postgraduate enrollment numbers between genders across different programs, which answers our research question and invalidates the null hypothesis. This finding suggests that gender distribution varies significantly among different postgraduate programs, warranting further investigation into the factors contributing to these disparities.

With the statistical analysis complete, we've identified significant differences in gender distribution across postgraduate programs. The next steps in our research could involve:

This comprehensive approach will provide a deeper understanding of the factors influencing postgraduate enrollment and help in formulating strategies to achieve a more balanced gender representation in higher education.

Given the completion of statistical analysis and the identification of significant gender disparities in postgraduate enrollments, the analysis has reached a natural conclusion point. Further exploration into the reasons behind these disparities and potential interventions would require a shift towards qualitative research methods, policy analysis, and strategic planning, which goes beyond the scope of this data-driven analysis.

To continue the analysis, one would typically move towards implementing the suggested next steps, such as conducting further statistical or qualitative research, reviewing educational policies, and developing actionable recommendations. However, these activities involve processes and methodologies that are not directly related to data analysis and thus fall outside the capabilities of this platform.

If you have any more data-driven questions or need assistance with a different analysis, feel free to ask!