In 2013, Gallup surveyed a nationally representative sample of 2027 adults about their soda consumption. The survey showed that 24% mostly drank diet soda. Based on the results, what is a 95% confidence interval for the proportion of American adults who mostly drink diet soda?

Question

Quizplus · Accepted Answer

We can use the formula for calculating a confidence interval for a proportion:
point estimate ± margin of error
where the point estimate is the sample proportion and the margin of error depends on the level of confidence and the sample size. For a 95% confidence interval, the margin of error is approximately 1.96 times the standard error, where the standard error is given by:

SE = sqrt((p * (1 - p))/n)
where p is the sample proportion and n is the sample size.

Using the given information, we have:
p = 0.24
n = 2027

SE = sqrt((0.24 * (1 - 0.24))/2027) = 0.0094 (rounded to 4 decimal places)

Therefore, the 95% confidence interval is:
0.24 ± (1.96 * 0.0094) = 0.24 ± 0.0184 (rounded to 4 decimal places)

This means we can be 95% confident that the true proportion of American adults who mostly drink diet soda falls within the range of 0.2216 to 0.2584. Choice B is the only option that falls within this range.

In 2013, Gallup Surveyed a Nationally Representative Sample of 2027