You are a researcher interested in studying the effect of different teaching methods on students' performance in a statistics course. You have designed an experiment where students are divided into three groups, each receiving instruction through a different teaching method: traditional lecture, online learning, and blended learning (a combination of traditional and online). After a semester, you collect the final exam scores of students from each group to determine if there are significant differences in their performance.
Question:
1. Formulate the null and alternative hypotheses for your study to test whether there are significant differences in the mean final exam scores among the three teaching methods.
2. Identify the appropriate statistical test to compare the mean final exam scores across the three teaching methods. Justify your choice and explain why it is suitable for this analysis.