In a study examining the effects of two different teaching methods on student performance, a high school math teacher decided to test the effectiveness of traditional lectures versus interactive online modules. To do this, she divided her class into two groups: Group A received instruction through traditional lectures, while Group B used interactive online modules. At the end of the semester, she evaluated the performance of both groups on a standardized test. The scores (out of 100) for each group were as follows:

• Group A (Traditional Lectures): 80, 75, 90, 70, 85
• Group B (Interactive Online Modules): 85, 90, 80, 88, 95

DO THE FOLLOWING:

1. State the null hypothesis (H0) and alternative hypothesis (H1).
2. Calculate the mean and standard deviation for each group.
3. Determine the appropriate hypothesis test
4. Determine the statistic.
5. Determine the degrees of freedom needed to interpret the t-statistic.
6. Conclude whether there is a significant difference between the two teaching methods based on the t-statistic and the degrees of freedom. Assume a significance level of 0.05