Using the chi-square to illuminate the gray areas:
In the last two examples (42% and 90%), it was pretty obvious what the chi-square test would say. In this last case, where 50% of sick days fall on M/F, it's not so obvious. This is a case where the statistical test can help resolve a gray area. Here goes...
You should have gotten a chi-square-calc of 4.166, compared to the chi-square-crit of 3.84. So, its a close call, but the test says that Dilbert's random sickday model probably does NOT hold up. The test can't tell you this for sure, but it still gives you an objective way to say "(probably) yes" or "(probably) no" when you're in a "gray" area.
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