Example 21.4

EXAMPLE 4 How confidence intervals behave

The Gallup sample of 1009 adult Americans in 2015 found that 616 reported actively trying to avoid drinking regular soda or pop, so the sample proportion was

and the 95% confidence interval was

Draw a second sample from the same population. It finds that 700 of its 1009 respondents reported actively trying to avoid drinking regular soda or pop. For this sample,

501

Figure 21.3: Figure 21.3 Repeated samples from the same population give different 95% confidence intervals, but 95% of these intervals capture the true population proportion p.

Draw another sample. Now the count is 598 and the sample proportion and confidence interval are

Keep sampling. Each sample yields a new estimate and a new confidence interval. If we sample forever, 95% of these intervals capture the true parameter. This is true no matter what the true value is. Figure 21.3 summarizes the behavior of the confidence interval in graphical form.