That depends on your level of uncertainty in your values. Your decision may not be satisfactory to another person.
This is really a statistics question about data analysis than about chemistry.
In any experiment or survey a valid "Null Hypothesis" has to be stated that can be answered by calculations on the obtained data.
In this case it would be "The data do NOT show any significant difference from a random distribution." We state it this way because disproving it means that there is a statistically significant correlation (still not necessarily causal).
The "proof" is where the degree of confidence in your answer comes in. The statistical test only compares your set of data to a random normal distribution curve. The value returned is compared to a value determined by the level of confidence that you want to have in your answer. That may vary from one researcher to another, although some common 'expected' standards may apply.