EXAMPLE 5 A 99% confidence interval

The Gallup random sample of 1009 adult Americans in 2015 found that 616 reported actively trying to avoid drinking regular soda or pop. We want a 99% confidence interval for the proportion p of all adult Americans who actively avoided drinking regular soda or pop. Table 21.1 says that for 99% confidence, we must go out z* = 2.58 standard deviations. Here are our calculations:

= 0.611 ± (2.58)(0.0153)

= 0.611 ± 0.0395

= 0.5715 to 0.6505

We are 99% confident that the true population proportion is between 57.15% and 65.05%. That is, we got this range of percentages by using a method that gives a correct answer 99% of the time.