TABLE 12-9
Four Surgical Procedures Currently Are Used to Install

Short Answer

TABLE 12-9
Four surgical procedures currently are used to install pacemakers. If the patient does not need to return for follow-up surgery the operation is called a "clear" operation. A heart center wants to compare the proportion of clear operations for the 4 procedures, and collects the following numbers of patients from their own records:
$$\begin{array}{l}\text {\quad\quad\quad\quad\quad\quad\quad Procedure }\\\begin{array} { l | r r r r | r } & \text { A } & \text { B } & \text { C } & \text { D } & \text { Total } \\\hline \text { Clear } & 27 & 41 & 21 & 7 & 96 \\\text { Return } & 11 & 15 & 9 & 11 & 46 \\\hline \text { Total } & 38 & 56 & 30 & 18 & 142\end{array}\end{array}$$ They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a level of significance of 0.05.
-Referring to Table 12-9, the test will involve ______degrees of freedom.