Answer :
Sure, I'll show you how to convert the given frequency table into a conditional relative frequency table by row. The process involves calculating the relative frequencies for each category by dividing each frequency by its respective row total.
Here is the original frequency table for reference:
[tex]\[ \begin{array}{|c|c|c|c|} \hline \text{Television Viewing Method} & \text{Average Household Age Under 40} & \text{Average Household Age 40 or Older} & \text{Total} \\ \hline \text{Internet} & 54 & 23 & 77 \\ \hline \text{Cable} & 81 & 92 & 173 \\ \hline \text{Total} & 135 & 115 & 250 \\ \hline \end{array} \][/tex]
### Step-by-step Solution:
1. Calculate the conditional relative frequency for each category in the "Internet" row:
- For Average Household Age Under 40:
[tex]\[ \frac{54}{77} \approx 0.7013 \][/tex]
- For Average Household Age 40 or Older:
[tex]\[ \frac{23}{77} \approx 0.2987 \][/tex]
2. Calculate the conditional relative frequency for each category in the "Cable" row:
- For Average Household Age Under 40:
[tex]\[ \frac{81}{173} \approx 0.4682 \][/tex]
- For Average Household Age 40 or Older:
[tex]\[ \frac{92}{173} \approx 0.5318 \][/tex]
### Conditional Relative Frequency Table by Row:
[tex]\[ \begin{array}{|c|c|c|} \hline \text{Television Viewing Method} & \text{Average Household Age Under 40} & \text{Average Household Age 40 or Older} \\ \hline \text{Internet} & 0.7013 & 0.2987 \\ \hline \text{Cable} & 0.4682 & 0.5318 \\ \hline \end{array} \][/tex]
In this table, each entry represents the proportion of households within each viewing method category, relative to the specific viewing method row totals. This conversion allows for a more insightful comparison of the distribution of household ages between different viewing methods.
Here is the original frequency table for reference:
[tex]\[ \begin{array}{|c|c|c|c|} \hline \text{Television Viewing Method} & \text{Average Household Age Under 40} & \text{Average Household Age 40 or Older} & \text{Total} \\ \hline \text{Internet} & 54 & 23 & 77 \\ \hline \text{Cable} & 81 & 92 & 173 \\ \hline \text{Total} & 135 & 115 & 250 \\ \hline \end{array} \][/tex]
### Step-by-step Solution:
1. Calculate the conditional relative frequency for each category in the "Internet" row:
- For Average Household Age Under 40:
[tex]\[ \frac{54}{77} \approx 0.7013 \][/tex]
- For Average Household Age 40 or Older:
[tex]\[ \frac{23}{77} \approx 0.2987 \][/tex]
2. Calculate the conditional relative frequency for each category in the "Cable" row:
- For Average Household Age Under 40:
[tex]\[ \frac{81}{173} \approx 0.4682 \][/tex]
- For Average Household Age 40 or Older:
[tex]\[ \frac{92}{173} \approx 0.5318 \][/tex]
### Conditional Relative Frequency Table by Row:
[tex]\[ \begin{array}{|c|c|c|} \hline \text{Television Viewing Method} & \text{Average Household Age Under 40} & \text{Average Household Age 40 or Older} \\ \hline \text{Internet} & 0.7013 & 0.2987 \\ \hline \text{Cable} & 0.4682 & 0.5318 \\ \hline \end{array} \][/tex]
In this table, each entry represents the proportion of households within each viewing method category, relative to the specific viewing method row totals. This conversion allows for a more insightful comparison of the distribution of household ages between different viewing methods.
