A city police chief decides to do an annual review of the police department by checking the number of monthly complaints
If the total number of complaints in each of the 12 months were 15, 18, 13, 12, 16, 20, 5, 10, 9, 11, 8, and 3 and the police chief wants a 90% confidence level, are the complaints in control?
From Table S6.2 z = 1.65
c-bar = (15 + 18 + 13 + 12 + 16 + 20 + 5 + 10 + 9 + 11 + 8 +3 )/12 = 11.67 complaints
UCL= 11.67+ 5.6366 = 17.307 complaints
LCL= 11.67 - 5.6366 = 6.033 complaints
Since 18 and 20 complaints fall above the UCL, while 5 and 3 complaints fall below the LCL, the complaints are not in control.
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