Answer :
Certainly! Let's go through each part of the question step-by-step.
### Part A: Percentage of Survey Respondents Who Do Not Like Both Hamburgers and Burritos
To determine the percentage of respondents who do not like both hamburgers and burritos, we need to analyze the given data in the table.
1. Total number of survey respondents: [tex]\(205\)[/tex].
2. Number of respondents who do not like both hamburgers and burritos: [tex]\(54\)[/tex].
To find the percentage:
[tex]\[ \text{Percentage not liking both} = \left( \frac{\text{Number of respondents not liking both}}{\text{Total respondents}} \right) \times 100 \][/tex]
[tex]\[ \text{Percentage not liking both} = \left( \frac{54}{205} \right) \times 100 \approx 26.34\% \][/tex]
Thus, approximately 26.34% of the survey respondents do not like both hamburgers and burritos.
### Part B: Marginal Relative Frequency of Customers That Like Hamburgers
Marginal relative frequency is a measure of how often a specific outcome occurs out of the total observations. Here, we need to find the frequency of respondents who like hamburgers out of the total respondents:
1. Total number of respondents: [tex]\(205\)[/tex].
2. Number of respondents who like hamburgers: [tex]\(110\)[/tex].
To find the marginal relative frequency of customers who like hamburgers:
[tex]\[ \text{Marginal relative frequency (likes hamburgers)} = \left( \frac{\text{Number of respondents liking hamburgers}}{\text{Total respondents}} \right) \times 100 \][/tex]
[tex]\[ \text{Marginal relative frequency (likes hamburgers)} = \left( \frac{110}{205} \right) \times 100 \approx 53.66\% \][/tex]
Thus, the marginal relative frequency of customers who like hamburgers is approximately 53.66%.
### Part C: Conditional Relative Frequencies and Strongest Association
We need to determine the strongest association between liking burritos and another factor (either liking hamburgers or not liking hamburgers). This involves calculating the conditional relative frequencies:
1. Number of respondents who like both hamburgers and burritos: [tex]\(29\)[/tex].
2. Number of respondents who like burritos but do not like hamburgers: [tex]\(41\)[/tex].
3. Total number of respondents who like burritos: [tex]\(70\)[/tex] (sum of respondents who like both and who like burritos but not hamburgers).
Let's calculate the conditional relative frequencies:
- For those who like burritos and hamburgers:
[tex]\[ \text{Conditional (likes both)} = \frac{\text{Number of respondents liking both}}{\text{Total respondents liking burritos}} \][/tex]
[tex]\[ \text{Conditional (likes both)} = \frac{29}{70} \approx 0.414 (or 41.4\%) \][/tex]
- For those who like burritos but do not like hamburgers:
[tex]\[ \text{Conditional (likes burritos but not hamburgers)} = \frac{\text{Number of respondents liking burritos but not hamburgers}}{\text{Total respondents liking burritos}} \][/tex]
[tex]\[ \text{Conditional (likes burritos but not hamburgers)} = \frac{41}{70} \approx 0.586 (or 58.6\%) \][/tex]
### Conclusion: Strongest Association
The strongest association is indicated by the higher conditional relative frequency.
- The conditional relative frequency for liking burritos and liking hamburgers is approximately 41.4%.
- The conditional relative frequency for liking burritos but not liking hamburgers is approximately 58.6%.
Therefore, there is a stronger association between "liking burritos and not liking hamburgers" as the conditional relative frequency is higher for that group. This means that among those who like burritos, a larger proportion does not like hamburgers.
Thus, the strongest association is "liking burritos and does not like hamburgers."
### Part A: Percentage of Survey Respondents Who Do Not Like Both Hamburgers and Burritos
To determine the percentage of respondents who do not like both hamburgers and burritos, we need to analyze the given data in the table.
1. Total number of survey respondents: [tex]\(205\)[/tex].
2. Number of respondents who do not like both hamburgers and burritos: [tex]\(54\)[/tex].
To find the percentage:
[tex]\[ \text{Percentage not liking both} = \left( \frac{\text{Number of respondents not liking both}}{\text{Total respondents}} \right) \times 100 \][/tex]
[tex]\[ \text{Percentage not liking both} = \left( \frac{54}{205} \right) \times 100 \approx 26.34\% \][/tex]
Thus, approximately 26.34% of the survey respondents do not like both hamburgers and burritos.
### Part B: Marginal Relative Frequency of Customers That Like Hamburgers
Marginal relative frequency is a measure of how often a specific outcome occurs out of the total observations. Here, we need to find the frequency of respondents who like hamburgers out of the total respondents:
1. Total number of respondents: [tex]\(205\)[/tex].
2. Number of respondents who like hamburgers: [tex]\(110\)[/tex].
To find the marginal relative frequency of customers who like hamburgers:
[tex]\[ \text{Marginal relative frequency (likes hamburgers)} = \left( \frac{\text{Number of respondents liking hamburgers}}{\text{Total respondents}} \right) \times 100 \][/tex]
[tex]\[ \text{Marginal relative frequency (likes hamburgers)} = \left( \frac{110}{205} \right) \times 100 \approx 53.66\% \][/tex]
Thus, the marginal relative frequency of customers who like hamburgers is approximately 53.66%.
### Part C: Conditional Relative Frequencies and Strongest Association
We need to determine the strongest association between liking burritos and another factor (either liking hamburgers or not liking hamburgers). This involves calculating the conditional relative frequencies:
1. Number of respondents who like both hamburgers and burritos: [tex]\(29\)[/tex].
2. Number of respondents who like burritos but do not like hamburgers: [tex]\(41\)[/tex].
3. Total number of respondents who like burritos: [tex]\(70\)[/tex] (sum of respondents who like both and who like burritos but not hamburgers).
Let's calculate the conditional relative frequencies:
- For those who like burritos and hamburgers:
[tex]\[ \text{Conditional (likes both)} = \frac{\text{Number of respondents liking both}}{\text{Total respondents liking burritos}} \][/tex]
[tex]\[ \text{Conditional (likes both)} = \frac{29}{70} \approx 0.414 (or 41.4\%) \][/tex]
- For those who like burritos but do not like hamburgers:
[tex]\[ \text{Conditional (likes burritos but not hamburgers)} = \frac{\text{Number of respondents liking burritos but not hamburgers}}{\text{Total respondents liking burritos}} \][/tex]
[tex]\[ \text{Conditional (likes burritos but not hamburgers)} = \frac{41}{70} \approx 0.586 (or 58.6\%) \][/tex]
### Conclusion: Strongest Association
The strongest association is indicated by the higher conditional relative frequency.
- The conditional relative frequency for liking burritos and liking hamburgers is approximately 41.4%.
- The conditional relative frequency for liking burritos but not liking hamburgers is approximately 58.6%.
Therefore, there is a stronger association between "liking burritos and not liking hamburgers" as the conditional relative frequency is higher for that group. This means that among those who like burritos, a larger proportion does not like hamburgers.
Thus, the strongest association is "liking burritos and does not like hamburgers."
