Instruction 15-6
Four Surgical Procedures Currently Are Used to Install

Instruction 15-6
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 centre wants to compare the proportion of clear operations for the four procedures, and collects the following numbers of patients from their own records:
| Procedure |
$$\begin{array} { | l | c | c | c | c | c | } \hline & \text { A } & \text { B } & \text { C } & \text { D } & \text { Total } \\\hline \text { Clear } & 27 & 41 & 21 & 7 & 96 \\\hline \text { Return } & 11 & 15 & 9 & 11 & 46 \\\hline \text { Total } & 38 & 56 & 30 & 18 & 142 \\\hline\end{array}$$ They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a 0.05 level of significance.
-Referring to Instruction 15-6,the test will involve _______ degree(s)of freedom.