A teacher figures that final grades in the statistics department are distributed as: A, 25%; B, 25%; C, 40%; D, 5%; F, 5%. At the end of a randomly selected semester, the following number of grades were recorded. Calculate
The chi-square test statistic χ $$x ^ { 2 }$$ to determine if the grade distribution for the department is different than
Expected. $$\begin{array} { l | l l l l l }
\text { Grade } & \text { A } & \text { B } & \text { C } & \text { D } & \text { F } \
\hline \text { Number } & 36 & 42 & 60 & 8 & 14
\end{array}$$
A)5.25
B)6.87
C)3.41
D)4.82

Question

A teacher figures that final grades in the statistics department are distributed as: A, 25%; B, 25%; C, 40%; D, 5%; F, 5%. At the end of a randomly selected semester, the following number of grades were recorded. Calculate
The chi-square test statistic χ $$x ^ { 2 }$$ to determine if the grade distribution for the department is different than
Expected. $$\begin{array} { l | l l l l l } 
\text { Grade } & \text { A } & \text { B } & \text { C } & \text { D } & \text { F } \
\hline \text { Number } & 36 & 42 & 60 & 8 & 14
\end{array}$$
A)5.25
B)6.87
C)3.41
D)4.82

Quizplus · Accepted Answer

The chi-square test statistic is calculated as:$$\chi^2 = \sum_{i=1}^k \frac{(O_i - E_i)^2}{E_i}$$where O_i is the observed frequency for category i, E_i is the expected frequency for category i, and k is the number of categories.In this case, we have:$$\chi^2 = \frac{(36 - 31.25)^2}{31.25} + \frac{(42 - 31.25)^2}{31.25} + \frac{(60 - 50)^2}{50} + \frac{(8 - 6.25)^2}{6.25} + \frac{(14 - 6.25)^2}{6.25} = 5.25$$Therefore, the chi-square test statistic is 5.25.

A Teacher Figures That Final Grades in the Statistics Department x2x ^ { 2 }x2

A Teacher Figures That Final Grades in the Statistics Department $x ^ { 2 }$