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) $n\hat{p}(1-\hat{p}) = 1748 \times 0.540 \times 0.46 = 434.2032$
Since 434.2032 $\geq$ 10, condition 1 holds true
ii) In this question, the sample consists of adult Americans, who are 18 or older and do not have a tattoo. Since there are over 1,000,000 adult Americans who are 18 or older and do not have a tattoo, 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.
