Answer :
Let's complete the two-way table by calculating the relative frequencies step-by-step:
1. Relative frequencies for the "Voted" row:
- Support: To calculate the relative frequency of those who voted and supported, we divide the number who supported by the total number who voted:
[tex]\[ \frac{18}{25} = 0.72 \text{ or } 72\% \][/tex]
- Oppose: To calculate the relative frequency of those who voted and opposed, we divide the number who opposed by the total number who voted:
[tex]\[ \frac{7}{25} = 0.28 \text{ or } 28\% \][/tex]
- Total: Since we are calculating the relative frequency for the total of those who voted (which includes both supporters and opposers), it will always be:
[tex]\[ \frac{25}{25} = 1 \text{ or } 100\% \][/tex]
2. Relative frequencies for the "Did Not Vote" row:
- Support: To calculate the relative frequency of those who did not vote but supported, we divide the number who supported by the total number who did not vote:
[tex]\[ \frac{13}{25} = 0.52 \text{ or } 52\% \][/tex]
- Oppose: To calculate the relative frequency of those who did not vote and opposed, we divide the number who opposed by the total number who did not vote:
[tex]\[ \frac{12}{25} = 0.48 \text{ or } 48\% \][/tex]
- Total: The relative frequency for the total of those who did not vote is:
[tex]\[ \frac{25}{25} = 1 \text{ or } 100\% \][/tex]
3. Relative frequencies for the "Total" row:
- Support: To calculate the relative frequency of the total number of supporters regardless of whether they voted or not, we divide the total number who supported by the overall total:
[tex]\[ \frac{31}{50} = 0.62 \text{ or } 62\% \][/tex]
- Oppose: To calculate the relative frequency of the total number of opposers regardless of whether they voted or not, we divide the total number who opposed by the overall total:
[tex]\[ \frac{19}{50} = 0.38 \text{ or } 38\% \][/tex]
- Total: The relative frequency for the overall total will always be:
[tex]\[ \frac{50}{50} = 1 \text{ or } 100\% \][/tex]
Now, we can complete the blank table with the calculated relative frequencies:
[tex]\[ \begin{tabular}{|l|c|c|c|} \cline { 2 - 4 } \multicolumn{1}{c|}{} & Support & Oppose & Total \\ \hline Voted & 72\% & 28\% & 100\% \\ \hline \begin{tabular}{l} Did Not \\ Vote \end{tabular} & 52\% & 48\% & 100\% \\ \hline Total & 62\% & 38\% & 100\% \\ \hline \end{tabular} \][/tex]
In summary:
- 72\% of those who voted supported the proposal.
- 28\% of those who voted opposed the proposal.
- 52\% of those who did not vote supported the proposal.
- 48\% of those who did not vote opposed the proposal.
- Overall, 62\% of all participants supported the proposal.
- Overall, 38\% of all participants opposed the proposal.
1. Relative frequencies for the "Voted" row:
- Support: To calculate the relative frequency of those who voted and supported, we divide the number who supported by the total number who voted:
[tex]\[ \frac{18}{25} = 0.72 \text{ or } 72\% \][/tex]
- Oppose: To calculate the relative frequency of those who voted and opposed, we divide the number who opposed by the total number who voted:
[tex]\[ \frac{7}{25} = 0.28 \text{ or } 28\% \][/tex]
- Total: Since we are calculating the relative frequency for the total of those who voted (which includes both supporters and opposers), it will always be:
[tex]\[ \frac{25}{25} = 1 \text{ or } 100\% \][/tex]
2. Relative frequencies for the "Did Not Vote" row:
- Support: To calculate the relative frequency of those who did not vote but supported, we divide the number who supported by the total number who did not vote:
[tex]\[ \frac{13}{25} = 0.52 \text{ or } 52\% \][/tex]
- Oppose: To calculate the relative frequency of those who did not vote and opposed, we divide the number who opposed by the total number who did not vote:
[tex]\[ \frac{12}{25} = 0.48 \text{ or } 48\% \][/tex]
- Total: The relative frequency for the total of those who did not vote is:
[tex]\[ \frac{25}{25} = 1 \text{ or } 100\% \][/tex]
3. Relative frequencies for the "Total" row:
- Support: To calculate the relative frequency of the total number of supporters regardless of whether they voted or not, we divide the total number who supported by the overall total:
[tex]\[ \frac{31}{50} = 0.62 \text{ or } 62\% \][/tex]
- Oppose: To calculate the relative frequency of the total number of opposers regardless of whether they voted or not, we divide the total number who opposed by the overall total:
[tex]\[ \frac{19}{50} = 0.38 \text{ or } 38\% \][/tex]
- Total: The relative frequency for the overall total will always be:
[tex]\[ \frac{50}{50} = 1 \text{ or } 100\% \][/tex]
Now, we can complete the blank table with the calculated relative frequencies:
[tex]\[ \begin{tabular}{|l|c|c|c|} \cline { 2 - 4 } \multicolumn{1}{c|}{} & Support & Oppose & Total \\ \hline Voted & 72\% & 28\% & 100\% \\ \hline \begin{tabular}{l} Did Not \\ Vote \end{tabular} & 52\% & 48\% & 100\% \\ \hline Total & 62\% & 38\% & 100\% \\ \hline \end{tabular} \][/tex]
In summary:
- 72\% of those who voted supported the proposal.
- 28\% of those who voted opposed the proposal.
- 52\% of those who did not vote supported the proposal.
- 48\% of those who did not vote opposed the proposal.
- Overall, 62\% of all participants supported the proposal.
- Overall, 38\% of all participants opposed the proposal.
