## Problem Statement:

This statistical analysis homework aims to investigate the influence of gender and learning modality on students' English scores. The study employs a 2x3 ANOVA to address the following research questions: (1) Do English scores differ between male and female students? (2) Do English scores differ across various learning modalities? (3) Is there an interaction between a student's gender and their chosen learning modality, affecting their English scores? The null and alternative hypotheses have been formulated for each of these research questions, and a two-way ANOVA will be conducted to test these hypotheses, as it is deemed suitable for analyzing the relationship between gender, learning modality, and English scores in this study.

### Solution

**Research Questions:
**

This study is designed as a 2x3 ANOVA (Analysis of Variance) to address the following research questions:

**Gender Effects:**Do the mean English scores differ between male and female students?**Learning Modality Effects:**Do the mean English scores differ across various learning modalities?**Interaction Effects:**Is there an interaction between a student's gender and their chosen learning modality, affecting their English scores?

**Hypotheses:
**

**For the Gender Main Effects:
**

**Null Hypothesis (H0):**There is no significant difference in English scores between male and female students.**Alternative Hypothesis (H1):**There is a significant difference in English scores between male and female students.

**For the Learning Modality Main Effects:
**

**Null Hypothesis (H0):**There is no significant difference in English scores among different learning modalities.**Alternative Hypothesis (H1):**At least one of the mean English scores differs from the others among the various learning modalities.

**For Interaction Effects:
**

**Null Hypothesis (H0):**There is no interaction between a student's gender and their chosen learning modality.**Alternative Hypothesis (H1):**There is an interaction between a student's gender and their chosen learning modality, affecting their English scores.

**Statistical Analysis:
**

To test these hypotheses, we will perform a two-way ANOVA, a powerful statistical test appropriate for our study. The choice of this test is justified by the presence of three variables for each participant: two categorical factors (gender and learning modality) and one dependent variable (English scores). The two factors divide the cases into distinct groups, and the dependent variable has an interval level of measurement. Our analysis will assess both the main effects of each factor (gender and learning modality) and the interaction between these two factors.