Answered

The frequency table represents the results of a survey comparing the average age of household members to the way that they watch non-network television.



\begin{table}

\captionsetup{labelformat=empty}

\caption{Television Viewing Method}


Average Household Age Under 40Average Household Age 40 or OlderTotal

Internet		542377

Cable		8192173

Total		135115250




\end{table}



Madigan converts the frequency table to a conditional relative frequency table by row.



\begin{table}

\captionsetup{labelformat=empty}

\caption{Television Viewing Method}


Average Household Age Under 40Average Household Age 40 or OlderTotal




\end{table}

Verified Answer :

  • Identify row totals for 'Internet' (77) and 'Cable' (173).
  • Divide each cell count by its respective row total to obtain relative frequencies.
  • Resulting table:
  • Internet: \(54/77 \approx 0.7013\), \(23/77 \approx 0.2987\)
  • Cable: \(81/173 \approx 0.4682\), \(92/173 \approx 0.5318\)
  • \(\boxed{\text{See Table in Step 3}}\)

Explanation

  1. Analyze the frequency table data

The initial data is provided in a frequency table representing the television viewing habits of 250 households, categorized by their average household age (Under 40 or 40 or Older) and their preferred viewing method (Internet or Cable).

  • Internet: 54 households Under 40, 23 households 40 or Older. Row total = 77.
  • Cable: 81 households Under 40, 92 households 40 or Older. Row total = 173.

A "conditional relative frequency table by row" transforms the raw counts into percentages or proportions, where the sum of each row equals 1 (or 100%). This allows us to compare the age distributions within each viewing category.

  1. Calculate conditional relative frequencies by row

To construct the row-conditional relative frequency table, we divide each cell frequency by its corresponding row total:

  1. For the Internet row (Total = 77):
  • Under 40: \(\frac{54}{77} \approx 0.7013\)
  • 40 or Older: \(\frac{23}{77} \approx 0.2987\)
  • Check: \(0.7013 + 0.2987 = 1.0000\)
  1. For the Cable row (Total = 173):
  • Under 40: \(\frac{81}{173} \approx 0.4682\)
  • 40 or Older: \(\frac{92}{173} \approx 0.5318\)
  • Check: \(0.4682 + 0.5318 = 1.0000\)
  1. Formulate the final table

The requested conditional relative frequency table is constructed by placing these calculated proportions into their respective rows and columns:

| | Average Household Age Under 40 | Average Household Age 40 or Older | Total |
| :--- | :--- | :--- | :--- |
| Internet | \(\approx 0.7013\) | \(\approx 0.2987\) | \(1.0\) |
| Cable | \(\approx 0.4682\) | \(\approx 0.5318\) | \(1.0\) |

This table shows the proportion of each age group within their respective television viewing method. For instance, roughly 70.13% of Internet users are Under 40, compared to about 46.82% of Cable users being in that same age bracket.

Examples

A marketing analyst uses this method to determine the demographic breakdown of their audience based on how they consume media. By normalizing the data to row totals, the company can clearly see the age distribution for different streaming platforms compared to traditional cable, regardless of the overall difference in total user count between those platforms. This helps in tailoring advertisements to specific age-based viewing patterns. For example, if they see that \(\frac{54}{77} \approx 70.13\%\) of internet viewers are young, they know where to focus their social media campaigns.

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