Final answer:
To calculate the 99% confidence interval for the true percentage of smokers of all people who completed 4 years of college, we can use a formula that incorporates the observed percentage, sample size, and the z-score for the desired confidence level. Plugging in the given values, the confidence interval is approximately (0.160, 0.206).
Step-by-step explanation:
To calculate the 99% confidence interval for the true percentage of smokers of all people who completed 4 years of college, we can use the formula:
CI = p ± Z * sqrt(p * (1-p)/n)
Where:
- CI is the confidence interval
- p is the observed percentage of smokers (18.3%, or 0.183)
- Z is the z-score corresponding to the desired confidence level (for 99% confidence, Z is approximately 2.576)
- n is the sample size (785)
Plugging in the values, we get:
CI = 0.183 ± 2.576 * sqrt(0.183 * (1-0.183)/785)
Simplifying, the confidence interval is approximately (0.160, 0.206).