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:

Step1: Understand conditional relative - frequency

Conditional relative - frequency is used to see if there is an association between two variables. If the conditional relative frequencies for different categories of one variable are different for different categories of the other variable, there is an association.

Step2: Analyze the given table

For meals prepared at home, the proportion of meals with ≥ 500 calories is 0.15, and for meals prepared at a restaurant, the proportion of meals with ≥ 500 calories is 0.55. These two values are quite different.

Step3: Evaluate the options

• Option 1: The values 0.55 and 0.45 are not the relevant ones to compare for association. We should compare the conditional relative frequencies for the same calorie - category across different preparation locations.
• Option 2: Since 0.15 (proportion of high - calorie meals at home) is not similar to 0.55 (proportion of high - calorie meals at a restaurant), there is an association between where the food is prepared and the number of calories. This option is correct.
• Option 3: The sum of each column being 1.0 is a property of conditional relative - frequency tables and does not indicate association.
• Option 4: The sum of rows not being 1.0 is not relevant to determining association in a conditional relative - frequency table.

Answer:

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