Question

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 | |---|---|---|---| | ≥ 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? - an association cannot be determined because the value 0.55 is similar to the value 0.45. - there is an association because the value 0.15 is not similar to the value 0.55. - there is an association because the sum of each column is 1.0. - an association cannot be determined because the sum of the rows going across is not 1.0.

Explanation:

To determine an association between meal preparation location (home/restaurant) and calorie count, we analyze conditional relative frequencies. For the "≥ 500 Calories" row, the frequency for home is 0.15 and for restaurant is 0.55. These values are not similar, indicating a difference in the likelihood of a meal having ≥ 500 calories based on preparation location.

• Option 1: 0.55 and 0.45 are from different rows (≥500 and <500 for restaurant), so comparing them is irrelevant. Eliminate.
• Option 2: 0.15 (home, ≥500) and 0.55 (restaurant, ≥500) are dissimilar, suggesting an association. Correct.
• Option 3: Column sums being 1.0 is a property of conditional relative frequency tables (by column), not evidence of an association. Eliminate.
• Option 4: Row sums (0.28 and 0.72) are marginal relative frequencies, and their sum not being 1.0 is normal (they sum to 1.0 overall: 0.28 + 0.72 = 1.0). Eliminate.

Answer:

There is an association because the value 0.15 is not similar to the value 0.55.