Final answer:
The null hypothesis in the scenario is that there is no significant difference in the means of the final exam scores between the three teaching methods. An ANOVA test can be used to determine if this hypothesis should be accepted or rejected, using a .05 significance level.
Step-by-step explanation:
To test whether teaching method affected student performance on the final exam, a statistical hypothesis test can be used. The null hypothesis for this scenario would be that there is no difference in the means of the final exam scores among the three teaching methods. In hypothesis testing, the null hypothesis is always the statement of no effect or no difference, which in this case translates to the assumption that the teaching method does not affect student performance.
Once data on the final exam scores from each group are collected, an ANOVA (Analysis of Variance) test could be implemented, considering the .05 significance level. If the p-value of the test statistic is less than .05, it would lead to the rejection of the null hypothesis, indicating that there is a statistically significant difference in final exam scores between at least two of the teaching methods. It's crucial that random sampling and random assignment to groups are maintained to support the validity of the results.