A jury presumes the defendat to be innocent (until proven guilty) and then looks at evidence that could invalidate that presumption. The more evidence the jury will see that invalidates the presumption of innocence, the more compelled they would feel to reject that presumption and conclude that the accused is guilty as charged. If the evidence is insufficient to pass the threshold of "beyond a reasonable doubt", then the jury will not be able to reject their initial presumption of the accuser's innocence in favour of his guilt.
A statistician presumes there is no effect/no difference and then looks at evidence in the data that could invalidate that presumption. The statistician weighs all the available evidence and comes up with a number (called p-value) which encapsulates the strength/weight of the evidence against the presumption of no effect/no difference. The number can be compared against the numeric equivalent of the threshold of "beyond a reasonable doubt" (e.g., 0.05). If the number falls beyond this threshold (i.e., the evidence is strong), the statistician will feel compelled to reject his initial presumption of no effect/no difference and conclude that the data provide evidence of an effect/difference.
Perhaps you can summarize the above parallelism visually with a side-by-side diagram. One shows the jury having to deliberate around the presumption of innocence, the other shows the statistician having to deliberate around the presumption of no effect/no difference. Both parties need to gather evidence that could invalidate this presumption and weigh its strength. The stronger the evidence, the more compelled each party would feel to reject their initial presumption and conclude that the opposite presumption must hold. The jury weighs the available evidence in more subjective ways - the statistician weighs the evidence in a more objective way via a single number. The smaller this number, the stronger the weight of evidence. Both parties must make a decision and reach a verdict/conclusion. While the jury can find the defendant not guilty, the statistician will generally abstain from concluding that there is no effect/no difference. The statistician will simply conclude there is no evidence in the data of an effect/difference, although it is possible in some cases to refine that statement.