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Sagot :
To analyze the given two-way frequency table, let's break down the problem into the two primary statements presented:
1. More people in the poll own a car than do not own one.
2. The total number of people in the poll who own a car is 4,120.
### Statement Analysis
Step-by-Step Analysis:
1. Total number of people who own a car:
From the table:
- LA residents who own a car: 3,251
- NYC residents who own a car: 1,478
Summing these values gives the total number of people who own a car:
[tex]\[ 3,251 + 1,478 = 4,729 \][/tex]
2. Total number of people who do not own a car:
From the table:
- LA residents who do not own a car: 869
- NYC residents who do not own a car: 6,182
Summing these values gives the total number of people who do not own a car:
[tex]\[ 869 + 6,182 = 7,051 \][/tex]
3. Total population surveyed:
From the table:
- Total LA residents surveyed: 4,120
- Total NYC residents surveyed: 7,660
Summing these values gives the total population surveyed:
[tex]\[ 4,120 + 7,660 = 11,780 \][/tex]
### Evaluating Statements:
1. More people in the poll own a car than do not own one:
- Number of people who own a car: 4,729
- Number of people who do not own a car: 7,051
Comparing these two numbers:
[tex]\[ 4,729 \quad (\text{own a car}) < 7,051 \quad (\text{do not own a car}) \][/tex]
This shows that fewer people own a car than do not own one, so this statement is false.
2. The total number of people in the poll who own a car is 4,120:
We already calculated that the total number of people who own a car is 4,729. Comparing:
[tex]\[ 4,729 \quad (\text{own a car}) \neq 4,120 \][/tex]
Therefore, this statement is also false since the actual total is 4,729, not 4,120.
### Conclusion:
Based on the analysis:
1. "More people in the poll own a car than do not own one." → False
2. "The total number of people in the poll who own a car is 4,120." → False
Thus, neither of the given statements about the two-way frequency table is true.
1. More people in the poll own a car than do not own one.
2. The total number of people in the poll who own a car is 4,120.
### Statement Analysis
Step-by-Step Analysis:
1. Total number of people who own a car:
From the table:
- LA residents who own a car: 3,251
- NYC residents who own a car: 1,478
Summing these values gives the total number of people who own a car:
[tex]\[ 3,251 + 1,478 = 4,729 \][/tex]
2. Total number of people who do not own a car:
From the table:
- LA residents who do not own a car: 869
- NYC residents who do not own a car: 6,182
Summing these values gives the total number of people who do not own a car:
[tex]\[ 869 + 6,182 = 7,051 \][/tex]
3. Total population surveyed:
From the table:
- Total LA residents surveyed: 4,120
- Total NYC residents surveyed: 7,660
Summing these values gives the total population surveyed:
[tex]\[ 4,120 + 7,660 = 11,780 \][/tex]
### Evaluating Statements:
1. More people in the poll own a car than do not own one:
- Number of people who own a car: 4,729
- Number of people who do not own a car: 7,051
Comparing these two numbers:
[tex]\[ 4,729 \quad (\text{own a car}) < 7,051 \quad (\text{do not own a car}) \][/tex]
This shows that fewer people own a car than do not own one, so this statement is false.
2. The total number of people in the poll who own a car is 4,120:
We already calculated that the total number of people who own a car is 4,729. Comparing:
[tex]\[ 4,729 \quad (\text{own a car}) \neq 4,120 \][/tex]
Therefore, this statement is also false since the actual total is 4,729, not 4,120.
### Conclusion:
Based on the analysis:
1. "More people in the poll own a car than do not own one." → False
2. "The total number of people in the poll who own a car is 4,120." → False
Thus, neither of the given statements about the two-way frequency table is true.
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