Final answer:
The fallacy in the statement is a hasty generalization, which draws conclusions from insufficient evidence.
Step-by-step explanation:
The logical fallacy used in the statement 'My cousin's school just changed to a six a.m. start time and everybody likes the change, that means an earlier start time would be good for our school' is a hasty generalization. This fallacy occurs when a conclusion is made based on insufficient evidence or a small sample size. In this statement, the conclusion is drawn from one school's experience without considering other variables or a broader set of data. It's important to avoid this fallacy by looking at a more comprehensive set of evidence before reaching a conclusion.