Economists at USF Are Researching the Problem of Absenteeism at U.S

Economists at USF are researching the problem of absenteeism at U.S. firms. A random sample of 100 U.S. organizations was selected to participate in a 1-year study. As part of the study, the economists had collected data on the following two variables for each company: shiftwork available (Yes or No), and union-management relationship (Good or Poor). As part of their analyses, the economists wanted to determine whether or not a company makes shiftwork available depends on the relationship between union and management. The collected data are shown below: $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$$\text {Relation}$
$\begin{array} { l c c c } \text { Shiftwork } & \text { Good } & \text { Bad } & \text { Total } \\ \text { No } & 11 & 22 & 33 \\ \text { Yes } & 25 & 42 & 67 \\ \text { Total } & 36 & 64 & 100 \end{array}$
In order to determine whether the shiftwork responses depend on the relationship responses, a two-way chi-square analysis should be conducted. When calculating the test statistic, what values for the expected counts should be used in the calculation?
A) $\mathrm { E } _ { 11 } = 11 , \mathrm { E } _ { 12 } = 22 , \mathrm { E } _ { 21 } = 25 , \mathrm { E } _ { 22 } = 42$
B) $\mathrm { E } _ { 11 } = 36 , \mathrm { E } _ { 12 } = 33 , \mathrm { E } _ { 21 } = 64 , \mathrm { E } _ { 22 } = 67$
C) $\mathrm { E } _ { 11 } = 11.88 , \mathrm { E } _ { 12 } = 21.12 , \mathrm { E } _ { 21 } = 24.12 , \mathrm { E } _ { 22 } = 42.88$
D) $\mathrm { E } _ { 11 } = 0.065 , \mathrm { E } _ { 12 } = 0.036 , \mathrm { E } _ { 21 } = 0.032 , \mathrm { E } _ { 22 } = 0.018$