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) $n\hat{p}(1-\hat{p}) > 10$
=1153 x 0.430 x 0.57
= 282.6003
Since $282.6003 \geq 10$, condition 1 holds true
ii) In this question, the sample consists of workers and retirees in the United States who are 25 and older. Since there are over 1,000,000 workers and retirees in the US who are 25 and older, we know our sample size is less than 5% of the population.
Thus, the requirements for constructing a confidence interval about p are satisfied.
