In an effort to study the effect of four different preventive maintenance programs on downtimes (in minutes) for a certain period of time in a production line, a factory runs four parallel production lines, and each line has five different types of machine. The different maintenance programs are randomly assigned to each of the four production lines so as to treat the various machines as blocks. Results are shown in Table 12.17.
Test the hypothesis, H0: True medians of the four maintenance programs are equal versus Ha: Not all are equal. State any assumptions you have made to solve this problem.
Table 12.17 Downtimes by Program

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Machine Method 1 Method 2 Method 3 Method 4 124 122 181 185 67 121 62 126 125 68 120 62 181 160 69 68 65 65 60