Asked by Miles Stewart on Jul 11, 2024
Verified
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. Day Mon Tue Wed Thur Fri Absences 3715122343\begin{array} { c | c c c c c } \text { Day } & \text { Mon } & \text { Tue } & \text { Wed } & \text { Thur } & \text { Fri } \\\hline \text { Absences } & 37 & 15 & 12 & 23 & 43\end{array} Day Absences Mon 37 Tue 15 Wed 12 Thur 23 Fri 43 Test statistic: χ2 = 28.308
P-value = 0.0000108
Test Statistic
A calculated value from sample data used to decide whether to reject the null hypothesis in the context of a statistical test.
Union Leader
A person who represents and advocates for the rights and interests of workers in negotiating with employers.
- Conduct chi-square tests to investigate hypotheses about the categorial data distribution.
- Implement significance levels for deducing outcomes in statistical tests.
Verified Answer
FC
Florita CardozaJul 12, 2024
Final Answer :
We reject the null hypothesis that absences occur on the different week days with the same frequencies.The standardized residuals are given by [2.157−2.157−2.746−0.5883.33]\left[ \begin{array} { l l l l l } 2.157 & - 2.157 & - 2.746 & - 0.588 & 3.33 ]\end{array} \right.[2.157−2.157−2.746−0.5883.33] . 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.
Learning Objectives
- Conduct chi-square tests to investigate hypotheses about the categorial data distribution.
- Implement significance levels for deducing outcomes in statistical tests.
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