This question is about interpreting the results of a survey and its margin of error in a confidence interval.

Key details from the problem:

• A survey of 4,220 adults in China aged 15+ finds that 30% smoke.
• The margin of sampling error is $\pm 1.9\%$ (95% confidence).
• The question asks which statement is accurate based on this result.

Explanation:

1. A 95% confidence interval (CI) means the actual percentage of adults who smoke in the population lies within the interval: $30\% \pm 1.9\% \implies [28.1\%, 31.9\%].$ This interval gives a range where the true percentage of smokers in the entire population is likely to fall.

2. Correct interpretation:

   • The CI is $[28.1\%, 31.9\%]$, so we are 95% confident that the percentage of all Chinese adults who smoke lies in this range.

3. Other options:

   • "Exactly 30% smoke": This is incorrect because the 30% is only the survey sample result, not the population parameter.
   • If the sample size were larger, the margin of error would likely decrease, not increase (this is a property of sample size and precision).
   • The statement about randomly sampling another group finding the same result is also false since survey results vary due to random sampling.

Correct Answer:

"We are 95% confident that 28.1% to 31.9% of all Chinese adults smoke."

Let me know if you'd like me to clarify further or explain sampling concepts in more detail!

Here are 5 related questions for you to consider:

1. What is a confidence interval, and how is it calculated?
2. How does increasing the sample size affect the margin of error?
3. Why is the population percentage not guaranteed to be 30%?
4. What does the term "95% confidence" actually mean?
5. How would results differ with a 99% confidence interval?

Tip: Remember, the margin of error only accounts for sampling variability, not for biases or errors in data collection.