Sure, let's go through the steps to complete the conditional relative frequency table based on the provided data.
Given the frequency table of hours worked per week on less than 1 acre and on 1 acre:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\cline{2-4}
& \text{hrs/wk} & \text{hrs/wk} & \text{Total} \\
\hline
<1 \text{ Acre} & 180 & 120 & 300 \\
\hline
1 \text{ Acre} & 40 & 160 & 200 \\
\hline
\text{Total} & 220 & 280 & 500 \\
\hline
\end{tabular}
\][/tex]
To create the conditional relative frequency table by row, we need to compute the relative frequencies for each row.
### Step 1: Calculate the conditional relative frequencies for "<1 Acre"
To find [tex]\( a \)[/tex] (hrs/wk for < 1 Acre):
[tex]\[ a = \frac{180}{300} = 0.6 \][/tex]
To find [tex]\( b \)[/tex] (hrs/wk for < 1 Acre):
[tex]\[ b = \frac{120}{300} = 0.4 \][/tex]
### Step 2: Calculate the conditional relative frequencies for "1 Acre"
To find [tex]\( c \)[/tex] (hrs/wk for 1 Acre):
[tex]\[ c = \frac{40}{200} = 0.2 \][/tex]
To find [tex]\( d \)[/tex] (hrs/wk for 1 Acre):
[tex]\[ d = \frac{160}{200} = 0.8 \][/tex]
### Step 3: Fill in the conditional relative frequency table
Now we can fill in the values into the conditional relative frequency table.
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline
& \text{0-3 hrs/wk} & \text{>3 hrs/wk} & \text{Total} \\
\hline
<1 \text{ Acre} & 0.6 & 0.4 & 1.0 \\
\hline
1 \text{ Acre} & 0.2 & 0.8 & 1.0 \\
\hline
\text{Total} & 0.44 & 0.56 & 1.0 \\
\hline
\end{tabular}
\][/tex]
Here, we've calculated the conditional relative frequencies for farmers working less than one acre of land and for farmers working one acre of land. The totals across each row sum to 1.0, which confirms that the values are correctly calculated as conditional relative frequencies.
