A company manager wishes to test a union leader's claim that absences occur on the different week days with the same frequencies.He compiled the following data. $$\begin{array}{cccccc}\text{ Day }& \text{ Mon }& \text{ Tue }& \text{ Wed }& \text{ Thur }& \text{ Fri }\\ \text{ Absences }& 37& 15& 12& 23& 43\end{array}$$ Test statistic: χ2 = 28.308
P-value = 0.0000108

We reject the null hypothesis that absences occur on the different week days with the same frequencies.The standardized residuals are given by $$[\begin{array}{lllll}2.157& -2.157& -2.746& -0.588& 3.33]\end{array}$$ . The largest residual is for the absences on Friday.This positive value,3.33,indicates that more absences occurred on Friday than predicted by the null hypothesis of uniform distribution.Similarly,but less dramatically,there were more absences than expected on Monday.There are large negative residuals for Tuesday and Wednesday,indicating that there were fewer absences than expected on these days.The manager might conclude that workers are more likely to use their sick or personal days on Monday or Friday when they can have a three-day weekend.