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 percentage points. which of the following is true based on the results of this survey?
if we were to randomly sample another group of 4,220 chinese adults we would find that exactly 30% of them smoke as well.
we are 95% confident that 26% to 34% of all chinese adults smoke.
if the sample size was larger, the margin of error would be larger as well.
we are 95% confident that 28% to 32% of all chinese adults smoke.
exactly 30% of all chinese adults smoke.

Explanation:

Step1: Recall the formula for confidence interval

The confidence interval is given by \(\hat{p}\pm E\), where \(\hat{p}\) is the sample proportion and \(E\) is the margin of error.

Step2: Identify the values

Here, \(\hat{p} = 30\%\) (or \(0.3\)) and \(E=2\%\) (or \(0.02\)).

Step3: Calculate the confidence interval

The lower limit is \(\hat{p}-E=30\% - 2\%=28\%\) and the upper limit is \(\hat{p}+E=30\%+ 2\%=32\%\)

Answer:

We are 95% confident that 28% to 32% of all Chinese adults smoke.