EXAMPLE 3 A confidence interval for soda consumption

The Gallup random sample of 1009 adult Americans found that 616 reported actively trying to avoid drinking regular soda or pop in 2015, a sample proportion . The 95% confidence interval for the proportion of all Americans who actively tried to avoid drinking regular soda or pop in 2015 is

= 0.611 ± (2)(0.01535)

= 0.611 ± 0.0307

= 0.5803 to 0.6417

Interpret this result as follows: we got this interval by using a recipe that catches the true unknown population proportion in 95% of all samples. The shorthand is: we are 95% confident that the true proportion of all Americans who actively tried to avoid drinking regular soda or pop in 2015 lies between 58.03% and 64.17%.