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) $n\hat{p}(1-\hat{p}) =1024 \times 0.75 \times 0.25 = 192$
Since $192 \geq 10$, condition 1 holds true
ii) In this question, the sample consists of adult Americans, who are 18 or older. Since there are over 1,000,000 adult Americans who are 18 or older, 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.
