Question

A 2011 Gallup survey based on telephone and face-to-face interviews with 4,220 adults in China, aged 15 and older suggests that 30% smoke regularly or occasionally. The following is also noted "one can say with 95% confidence that the maximum margin of sampling error is 2.2 percentage points". Which of the following is true based on the results of this survey?
A. If we were to randomly sample another group of 4,220 Chinese adults we would find that exactly 30% of them smoke as well.
B. If the sample size was larger, the margin of error would be larger as well.
C. Exactly 30% of all Chinese adults smoke.
D. We are 95% confident that 25.6% to 34.4% of all Chinese adults smoke.
E. We are 95% confident that 27.8% to 32.2% of all Chinese adults smoke.

Answer 1

Answer:

E. We are 95% confident that 27.8% to 32.2% of all Chinese adults smoke.

Step-by-step explanation:

x% confidence interval between a and b.

Interpretation: We are x% sure that the true value is between a and b.

In this question:

95% confidence level

30% with a margin of error of 2.2%.

So

30 - 2.2 = 27.8%

30 + 2.2 = 32.2%

So the correct answer is:

E. We are 95% confident that 27.8% to 32.2% of all Chinese adults smoke.