Explanatory Answer:
To construct a confidence interval for the population proportion of adults who believe in UFOs, we can use the following formula:
CI = p ± zsqrt(p(1-p)/n)
where:
CI is the confidence interval
p is the sample proportion
z* is the critical value from the standard normal distribution for the desired confidence level
n is the sample size
In this case, the sample proportion is p = 746/2276 = 0.3275. The sample size is n = 2276.
To find the critical value z* for a 99% confidence level, we can look up the value in a standard normal distribution table or use a calculator. The critical value for a 99% confidence level is approximately 2.576.
Substituting these values into the formula, we get:
CI = 0.3275 ± 2.576sqrt(0.3275(1-0.3275)/2276)
Simplifying the expression inside the square root, we get:
CI = 0.3275 ± 0.0225
Therefore, the 99% confidence interval for the population proportion of adults who believe in UFOs is:
CI = (0.305, 0.350)
This means that we are 99% confident that the true proportion of adults who believe in UFOs is between 0.305 and 0.350.