We would like to make conclusions about the difference in two population proportions: . We consider three examples. In the first, we compare the approval of the 2010 healthcare law under two different question phrasings. In the second application, a company weighs whether they should switch to a higher quality parts manufacturer. In the last example, we examine the cancer risk to dogs from the use of yard herbicides.
In our investigations, we first identify a reasonable point estimate of based on the sample. You may have already guessed its form: . Next, in each example we verify that the point estimate follows the normal model by checking certain conditions. Finally, we compute the estimate’s standard error and apply our inferential framework.