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 99.7% confidence that the maximum margin of sampling error is ±4 percentage points.”

Prompt

Based on this poll, 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. PLEASE TYPE!!

Answer 1

Solution:

Given: 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 responses were access (27%), cost (20%), obesity (14%), cancer (13%), government interference (3%), or the flu (less than 0.5%)

thus   = proportion of U.S. adults who feel that access to healthcare is the most urgent health problem facing this country

= 27%

n = 1012

We have to construct 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.

where

We need to find z_c value for c=95% confidence level.

Find Area = ( 1 + c ) / 2 = ( 1 + 0.95) /2 = 1.95 / 2 = 0.9750

Look in z table for Area = 0.9750 or its closest area and find z value.

Area = 0.9750 corresponds to 1.9 and 0.06 , thus z critical value = 1.96

That is : Z_c = 1.96

thus

Thus

Interpretation:

We are 95% confident that the true estimate of the percentage of U.S. adults who feel that access to healthcare is the most urgent health problem facing this country is between 24.3% and 29.7%