Question

A Gallup poll conducted in November of 2011 asked the following question, “What would you say is the most urgent health problem facing this country at the present time?” The choices were access, cost, obesity, cancer, government interference, or the flu. The responses were access (27%), cost (20%), obesity (14%), cancer (13%), government interference (3%), or the flu (less than 0.5%).

The following is an excerpt from the Survey Methods section. “Results for this Gallup poll are based on telephone interviews conducted Nov. 3-6, 2011, with a random sample of 1,012 adults ages 18 and older, living in all 50 U.S. states and the District of Columbia. For results based on a total sample of national adults, one can say with 95% confidence that the maximum margin of sampling error is ±4 percentage points.”

Prompt

If we accept the maximum margin of sampling error provided above, find a 95% confidence interval to estimate the percentage of U.S. adults who feel that access to healthcare is the most urgent health problem facing this country. Interpret your interval in context.

Answer 1

Solution:

In the given problem, we are given that responses to access is 27%. Therefore,

The 95% confidence interval to estimate the percentage of U.S. adults who feel that access to healthcare is the most urgent health problem facing this country is:

Where:

is the critical value at the 0.05 significance level

There is a 95% chance that the confidence interval calculated contains the true population proportion of U.S. adults who feel that access to healthcare is the most urgent health problem facing this country