A company operates four machines on three separate shirts daily. The following contingency table presents the data during a 6-month time period, concerning the machine breakdowns that resulted.

Suppose we are interested in determining whether a machine’s breakdown probability during a particular shift is influenced by that shift. In other words, we are interested in testing, for an arbitrary breakdown, whether the machine causing the breakdown and the shift on which the breakdown occurred are independent.

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Number of Breakdowns Machine A B C D Total per Shift Shift 1 Shift 2 Shift 3 Total per Machine 33 56 153 10 10 13 20 2238 12 24 6272 7 10 10 27 3533 50 138