Final answer:
The researcher does not need to sample more adult Americans in either case (a) or (b), as the conditions of the Central Limit Theorem are already met with the initial sample size.
Step-by-step explanation:
To determine how many more adult Americans a researcher needs to sample to say that the distribution of the sample proportion of adults who respond 'yes' is approximately normal, we must refer to the Central Limit Theorem. According to this theorem, the distribution of the sample proportion will be approximately normal if both np ≥ 10 and n(1-p) ≥ 10, where 'n' is the sample size and 'p' is the proportion of the population with the characteristic of interest.
(a) If 10% of all adult Americans support the changes (p = 0.10), then the researcher has already met the conditions since 50(0.10) = 5 and 50(0.90) = 45, both of which are less than 10. Therefore, the researcher does not need to sample more adult Americans.
(b) If 15% of all adult Americans support the changes (p = 0.15), then the conditions are 50(0.15) = 7.5 and 50(0.85) = 42.5. Since 7.5 is less than 10, the researcher still meets the condition. No additional sampling is needed; the researcher does not need to sample more adult Americans.
In conclusion, the researcher does not need to ask more American adults in both case (a) and case (b). It's important to round up these figures to the nearest integer when applying these rules, but in these cases, the sample size requirement is already satisfied.