Answer
The requirements for constructing a confidence interval about p are satisfied.
Work Step by Step
In order to construct a confidence interval it is required that:
i) $n\hat{p}(1-\hat{p}) \geq 10$
ii) The sample size is no more than 5% of the population size $(n \leq 0.05N)$
Testing the conditions:
i) $n\hat{p}(1-\hat{p}) =1050 \times 0.470 \times 0.53 = 261.555$
Since $261.555 \geq 10$, condition 1 holds true
ii) In this question, the sample consists of adult Americans. Since the population consists of over 1,000,000 adult Americans, we know our sample size is less than 5% of the population. Thus, condition 2 also holds true.
Thus, the requirements for constructing a confidence interval about p are satisfied.
