The conditional relative frequency table below was generated by column using frequency table data comparing the number of calories in a meal to whether the meal was prepared at home or at a restaurant.
Number of Calories and Location of Meal Preparation
| | Home | Restaurant | Total |
| :------------------- | :--- | :--------- | :---- |
| $\geq$ 500 Calories | 0.15 | 0.55 | 0.28 |
| < 500 Calories | 0.85 | 0.45 | 0.72 |
| Total | 1.0 | 1.0 | 1.0 |
A nutritionist attempts to determine an association between where food is prepared and the number of calories the food contains. Which is most likely true?
A. An association cannot be determined because the value 0.55 is similar to the value 0.45.
B. There is an association because the value 0.15 is not similar to the value 0.55.
C. There is an association because the sum of each column is 1.0.
D. An association cannot be determined because the sum of the rows going across is not 1.0.
Answer (2)
Analyze the conditional relative frequencies for meals with ≥ 500 calories: home (0.15) vs. restaurant (0.55).
Analyze the conditional relative frequencies for meals with < 500 calories: home (0.85) vs. restaurant (0.45).
Since the conditional relative frequencies differ significantly between home and restaurant for both calorie categories, there is an association.
The most accurate conclusion is: There is an association because the value 0.15 is not similar to the value 0.55. There is an association because the value 0.15 is not similar to the value 0.55 .
Explanation
Analyze the problem We are given a conditional relative frequency table that compares the number of calories in a meal to whether the meal was prepared at home or at a restaurant. The nutritionist wants to determine if there is an association between where food is prepared and the number of calories.
Determine the approach We need to analyze the values in the table to determine if there is a significant difference in the conditional relative frequencies between home and restaurant for both calorie categories. If the values are significantly different, there is an association. If they are similar, there is no association.
Analyze the values For meals with ≥ 500 calories, the conditional relative frequency for home is 0.15 and for restaurant is 0.55. These values are quite different. For meals with < 500 calories, the conditional relative frequency for home is 0.85 and for restaurant is 0.45. These values are also different.
Conclusion Since the conditional relative frequencies are significantly different between home and restaurant for both calorie categories, there is an association between where the food is prepared and the number of calories it contains. The option that best describes this is: There is an association because the value 0.15 is not similar to the value 0.55.
Examples
Understanding associations between food preparation location and calorie content can help nutritionists provide better dietary advice. For example, if restaurant meals are consistently higher in calories, people trying to manage their weight might be advised to cook at home more often. This kind of analysis is a foundation for making informed decisions about food choices and health.
There is an association between meal preparation location and calorie content due to significant differences in conditional relative frequency values. The association is illustrated by the fact that fewer meals prepared at home contain ≥ 500 calories compared to those from restaurants. Thus, the chosen answer is B.
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