No, that's not it at all.

What you would do is you would have a higher standard of proof. If you conduct a study with a 95% confidence interval that sugar doesn't increase excitement more than 5% then, you can say with 95% confidence the mean falls above that 5% threshold.

However in this study, that confidence intervals were all over the place (from huge effect on mood to negative effect on mood) which generally means you need more participants to conclude anything.