Answer :
Let's analyze the given data step-by-step and draw the required conclusions.
### Conclusion 1: Voters are more likely to participate in a presidential election than in a primary.
To verify this, we need to compare the average participation rates between the primaries and the general elections across the given states.
1. Calculate the average participation rate for the Republican Primaries:
[tex]\[ \text{Average Primary Participation} = \frac{12.8 + 16.5 + 1.4 + 22.9 + 12.8}{5} = \frac{66.4}{5} = 13.28\% \][/tex]
2. Calculate the average participation rate for the General Elections:
[tex]\[ \text{Average General Participation} = \frac{63.5 + 64.7 + 53.1 + 55.2 + 49.7}{5} = \frac{286.2}{5} = 57.24\% \][/tex]
Since [tex]\(57.24\% > 13.28\%\)[/tex], we conclude that voters are more likely to participate in a presidential election than in a primary.
### Conclusion 2: Texas and Florida have the same number of Republican voters.
Given the data:
- Texas Primary: [tex]\(12.8\%\)[/tex]
- Florida Primary: [tex]\(12.8\%\)[/tex]
Since both states have the same participation rate in the Republican Primaries, we conclude that Texas and Florida have the same number of Republican voters.
### Conclusion 3: Voters are more likely to participate in a primary than in a presidential election.
We have previously calculated the average participation rates:
- Primary Participation: [tex]\(13.28\%\)[/tex]
- General Participation: [tex]\(57.24\%\)[/tex]
Since [tex]\(13.28\% < 57.24\%\)[/tex], we conclude that voters are more likely to participate in a presidential election than in a primary, making this conclusion false.
### Conclusion 4: California has more Republicans than New York.
Given the data:
- California General: [tex]\(55.2\%\)[/tex]
- New York General: [tex]\(53.1\%\)[/tex]
Since [tex]\(55.2\% > 53.1\%\)[/tex], we conclude that California has more Republicans than New York.
### Summary
From the above analysis, the following conclusions are supported by the data:
1. Voters are more likely to participate in a presidential election than in a primary. (True)
2. Texas and Florida have the same number of Republican voters. (True)
3. Voters are more likely to participate in a primary than in a presidential election. (False)
4. California has more Republicans than New York. (True)
Thus, the supported conclusions based on the data are:
- Voters are more likely to participate in a presidential election than in a primary.
- Texas and Florida have the same number of Republican voters.
- California has more Republicans than New York.
### Conclusion 1: Voters are more likely to participate in a presidential election than in a primary.
To verify this, we need to compare the average participation rates between the primaries and the general elections across the given states.
1. Calculate the average participation rate for the Republican Primaries:
[tex]\[ \text{Average Primary Participation} = \frac{12.8 + 16.5 + 1.4 + 22.9 + 12.8}{5} = \frac{66.4}{5} = 13.28\% \][/tex]
2. Calculate the average participation rate for the General Elections:
[tex]\[ \text{Average General Participation} = \frac{63.5 + 64.7 + 53.1 + 55.2 + 49.7}{5} = \frac{286.2}{5} = 57.24\% \][/tex]
Since [tex]\(57.24\% > 13.28\%\)[/tex], we conclude that voters are more likely to participate in a presidential election than in a primary.
### Conclusion 2: Texas and Florida have the same number of Republican voters.
Given the data:
- Texas Primary: [tex]\(12.8\%\)[/tex]
- Florida Primary: [tex]\(12.8\%\)[/tex]
Since both states have the same participation rate in the Republican Primaries, we conclude that Texas and Florida have the same number of Republican voters.
### Conclusion 3: Voters are more likely to participate in a primary than in a presidential election.
We have previously calculated the average participation rates:
- Primary Participation: [tex]\(13.28\%\)[/tex]
- General Participation: [tex]\(57.24\%\)[/tex]
Since [tex]\(13.28\% < 57.24\%\)[/tex], we conclude that voters are more likely to participate in a presidential election than in a primary, making this conclusion false.
### Conclusion 4: California has more Republicans than New York.
Given the data:
- California General: [tex]\(55.2\%\)[/tex]
- New York General: [tex]\(53.1\%\)[/tex]
Since [tex]\(55.2\% > 53.1\%\)[/tex], we conclude that California has more Republicans than New York.
### Summary
From the above analysis, the following conclusions are supported by the data:
1. Voters are more likely to participate in a presidential election than in a primary. (True)
2. Texas and Florida have the same number of Republican voters. (True)
3. Voters are more likely to participate in a primary than in a presidential election. (False)
4. California has more Republicans than New York. (True)
Thus, the supported conclusions based on the data are:
- Voters are more likely to participate in a presidential election than in a primary.
- Texas and Florida have the same number of Republican voters.
- California has more Republicans than New York.
