Example 31

EXAMPLE 31 Bayes' Rule

The Gardasil vaccine

Table 24 contains a contingency table (crosstabulation) of the variables com-pleted and insurance type for the data set Gardasil.¹²

Table 5.57: Table 24 Contingency table of the variables completed and insurance type

			Insurance type
		Hospital- based	Medical assistance	Military	Private payer	Total
Completed	No	45	220	209	470	944
	Yes	39	55	122	253	469
	Total	84	275	331	723	1413

Define the following events:

Use Bayes’ Rule to find the probability that a randomly selected patient used military insurance, given that he or she completed the treatment.

Solution

We are interested in the probability . Substituting for and for in the formula for Bayes’ Rule, we obtain:

From Table 24, we have . The event consists of all other insurance types besides military. So we have , and . Thus,

Note that this result is confirmed by the direct calculation of using Table 24, which is the single cell of 122 military completers divided by the total number of completers.

NOW YOU CAN DO

Exercises 105–108.