Use the following set of observed frequencies to test the independence of the two variables.Variable one has values of 'A' and 'B'; variable two has values of 'C', 'D', and 'E'. $$\begin{array} { | l | l | l | l | }
\hline & \mathrm { C } & \mathrm { D } & \mathrm { E } \
\hline \mathrm { A } & 12 & 10 & 8 \
\hline \mathrm { B } & 20 & 24 & 26 \
\hline
\end{array}$$ Using $\alpha$ = 0.05, the estimates of the expected frequency in row 1 (A)column 1 (C)when the two variables are independent is _______.
A)9.6
B)12
C)16
D)10
E)20

Question

Use the following set of observed frequencies to test the independence of the two variables.Variable one has values of 'A' and 'B'; variable two has values of 'C', 'D', and 'E'. $$\begin{array} { | l | l | l | l | } 
\hline & \mathrm { C } & \mathrm { D } & \mathrm { E } \
\hline \mathrm { A } & 12 & 10 & 8 \
\hline \mathrm { B } & 20 & 24 & 26 \
\hline
\end{array}$$ Using $\alpha$ = 0.05, the estimates of the expected frequency in row 1 (A)column 1 (C)when the two variables are independent is _______.
A)9.6
B)12
C)16
D)10
E)20

Quizplus · Accepted Answer

To estimate the expected frequency for cell (A, C) under the assumption of independence, we use the formula: $$E_{ij} = \frac{(Row\ Total) \times (Column\ Total)}{Grand\ Total}$$. For cell (A, C), the row total for A is $12 + 10 + 8 = 30$, the column total for C is $12 + 20 = 32$, and the grand total is $12 + 10 + 8 + 20 + 24 + 26 = 100$. Thus, the expected frequency for cell (A, C) is $\frac{30 \times 32}{100} = 9.6$.

Use the Following Set of Observed Frequencies to Test the Independence