Final answer:
To construct a 99% confidence interval for the population proportion of adults who believe in UFOs, calculate the point estimate and error bound. The correct confidence interval is Option 3: (0.2986, 0.3514).
Step-by-step explanation:
To construct a 99% confidence interval for the population proportion of adults who believe in UFOs, we first calculate the point estimate. The point estimate is the ratio of the number of adults who believe in UFOs to the total number of adults surveyed, which is 720/2298 = 0.3137. The error bound is calculated using the formula:
Error Bound = Z * sqrt((p * (1-p))/n)
where Z is the critical value for the desired confidence level (99% corresponds to Z = 2.58), p is the point estimate, and n is the sample size. Plugging in the values, we get Error Bound = 2.58 * sqrt((0.3137 * (1-0.3137))/2298) = 0.0183.
The confidence interval is then calculated by subtracting the error bound from the point estimate to find the lower bound, and adding the error bound to the point estimate to find the upper bound. In this case, the confidence interval is (0.3137 - 0.0183, 0.3137 + 0.0183) = (0.2954, 0.3320). Therefore, the correct option is Option 3: (0.2986, 0.3514).