MathBench > Statistical Tests

Chi-square Tests

Dilbert’s 3 day work week

I want to start with some data and a model from outside of biology. The "data" (such as it is) comes from a Dilbert cartoon, and the competing hypotheses about the data come from Dilbert (the hard-working and long-suffering engineer) and his boss (the Evil Pointy-Haired Boss). We will work through a statistical test to show that Dilbert is right and the boss is wrong -- of course!

In this cartoon, Dilbert's evil pointy-haired boss decides he's found a new way that employees are cheating him: they are taking fake "sick days" on Mondays and Fridays in order to get longer weekends.

Dilbert cartoon

Before we get into statistics, take a moment to think about the situation: What proportion of sick days 'should' fall on Monday or Friday (assuming there are no patterns to when people get sick, and no one is abusing their sick days?)

What proportion of sick days 'should' fall on Monday or Friday (assuming there are no patterns to when people get sick, and no one is abusing their sickdays?)

 

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I think I have the answer: If people get sick randomly,
then they are equally likely to get sick on any day of the week.
Since 2/5 of workdays are either Monday or Friday,
that makes 40%.