Effectiveness of Teaching Methods Comparison

A group of researchers conducted a study to analyze the effectiveness of two different teaching methods, referred to as Method X and Method Y, on students' performance in mathematics. They tested both methods on two separate groups of 50 students each. The results were as follows:

Method X:

• Average score: 75
• Standard deviation: 10

Method Y:

• Average score: 82
• Standard deviation: 15

Using these results, the researchers conducted a hypothesis test to determine if the difference in average scores could be statistically significant. Assume the significance level of the test is 0.05.

Based on the data provided, determine the relationship between the effectiveness of the two methods of teaching.