Let's say that one possible side effect of the drug oxycodone is nausea. The makers of oxycodone are working with the FDA to determine if they need to list this as a "common side effect" or not. Let's say that the FDA states that nausea needs to be listed as a common side effect if it's experienced by at least 10% of users. If the makers do not want to list this as a side effect, then they need to provide evidence that the true proportion of users who experience nausea is less than 10%, and that this needs to be done at a significance level of 0.01. In a clinical study involving the drug, the research team identifies that 39 out of 460 patients reported nausea.

(a) Complete hypothesis test to determine if nausea needs to be listed as a common side effect.

(b) Let's say that the true proportion who experience nausea after taking Oxycodone is truly 8.5%. What could the research team do to increase the likelihood that they meet the FDA's evidence requirement?