ABSTRACT
Suppose we have a situation where each of n individuals has an independent choice. For example, drivers on State Route (SR) 91 in California have
a choice of driving on either a toll or free section of the roadway-both sections run parallel to each other. Suppose we use notation
Xi = 0 1
if option 1 is made if option 2 is made
= …, , , .i n1
For our example, 0 may correspond to a driver using the free lanes and a 1 would correspond to a driver using the tolled lanes. Let ˆ /P X nin i= ∑ =1 andp EP=
ˆ . In an analogous approach to testing whether a sample mean equals µ or not, we will test whether p p= 0 or not. With a couple of technical caveats that we will discuss later, the philosophy of testing proportions is analogous to those for testing means from a continuous random variable. One caveat is that we must have a minimum number of observations in order to make meaningful condence intervals. In this textbook we will assume that there are at least ve successes (ones) and at least ve failures (zeros) in any given trial.
