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Sagot :
To determine if an association exists between the location of meal preparation and the number of calories in the meal, we need to examine the relative frequencies given in the table.
Let’s break down the two rows in the table:
- The first row shows meals with ≥ 500 calories:
- When prepared at home, the relative frequency is 0.15.
- When prepared at a restaurant, the relative frequency is 0.55.
- The second row shows meals with < 500 calories:
- When prepared at home, the relative frequency is 0.85.
- When prepared at a restaurant, the relative frequency is 0.45.
To identify the association, we need to answer whether there is a significant difference between the conditional relative frequencies for home-prepared meals and restaurant-prepared meals.
### Evaluation:
- For meals with ≥ 500 calories, the relative frequencies are:
- 0.15 at home
- 0.55 at a restaurant
- For meals with < 500 calories, the relative frequencies are:
- 0.85 at home
- 0.45 at a restaurant
Given the noticeable difference (0.15 vs 0.55 and 0.85 vs 0.45), it clearly suggests an association. The large difference indicates that the number of calories in a meal is related to whether the meal was prepared at home or at a restaurant.
- The value 0.55 being much larger than 0.15 for meals with ≥ 500 calories implies that meals prepared at a restaurant are more likely to have ≥ 500 calories.
- Conversely, the value 0.85 being much larger than 0.45 for meals with < 500 calories suggests that meals prepared at home are more likely to have < 500 calories.
This significant variation implies that where the meal is prepared does have an impact on the number of calories it contains.
### Conclusion:
The most likely true statement is:
There is an association because the value 0.15 is not similar to the value 0.55.
Let’s break down the two rows in the table:
- The first row shows meals with ≥ 500 calories:
- When prepared at home, the relative frequency is 0.15.
- When prepared at a restaurant, the relative frequency is 0.55.
- The second row shows meals with < 500 calories:
- When prepared at home, the relative frequency is 0.85.
- When prepared at a restaurant, the relative frequency is 0.45.
To identify the association, we need to answer whether there is a significant difference between the conditional relative frequencies for home-prepared meals and restaurant-prepared meals.
### Evaluation:
- For meals with ≥ 500 calories, the relative frequencies are:
- 0.15 at home
- 0.55 at a restaurant
- For meals with < 500 calories, the relative frequencies are:
- 0.85 at home
- 0.45 at a restaurant
Given the noticeable difference (0.15 vs 0.55 and 0.85 vs 0.45), it clearly suggests an association. The large difference indicates that the number of calories in a meal is related to whether the meal was prepared at home or at a restaurant.
- The value 0.55 being much larger than 0.15 for meals with ≥ 500 calories implies that meals prepared at a restaurant are more likely to have ≥ 500 calories.
- Conversely, the value 0.85 being much larger than 0.45 for meals with < 500 calories suggests that meals prepared at home are more likely to have < 500 calories.
This significant variation implies that where the meal is prepared does have an impact on the number of calories it contains.
### Conclusion:
The most likely true statement is:
There is an association because the value 0.15 is not similar to the value 0.55.
Answer:
Step-by-step explanation:
We need to evaluate if the distribution of calorie counts is different between meals prepared at home and meals prepared at a restaurant.
For meals with ≥ 500 calories, the proportion is 0.15 for home-prepared meals and 0.55 for restaurant-prepared meals.
For meals with < 500 calories, the proportion is 0.85 for home-prepared meals and 0.45 for restaurant-prepared meals.
These differences are significant:
0.15 is quite different from 0.55.
0.85 is quite different from 0.45.
These differences suggest that there is an association between the location of meal preparation and the number of calories in the meal.
Now, let's evaluate the provided options:
A. An association cannot be determined because the value 0.55 is similar to the value 0.45.
This statement is incorrect because 0.55 and 0.45 are not similar in the context of this problem; they show a notable difference.
B. There is an association because the value 0.15 is not similar to the value 0.55.
This statement is correct. The large difference between 0.15 (home) and 0.55 (restaurant) for meals with ≥ 500 calories indicates an association.
C. There is an association because the sum of each column is 1.0.
This statement is incorrect. The sum of each column being 1.0 is a property of relative frequency tables and does not indicate an association.
D. An association cannot be determined because the sum of the rows going across is not 1.0.
This statement is incorrect. The sums of rows across are 1.0 (0.28 for ≥ 500 calories and 0.72 for < 500 calories), but the statement's logic is flawed since row sums are not the basis for determining associations in this context.
Thus, the correct answer is:
B. There is an association because the value 0.15 is not similar to the value 0.55.
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