Question

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.

Answer 1

Given the conditional relative frequency table below which 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

To determine whether there is an association between where food is prepared and the number of carories the food contain, we recall that an "association" exists between two categorical variables if the column conditional relative frequencies are different for the columns of the table. The bigger the differences in the conditional relative frequencies, the stronger the association between the variables. If the conditional relative frequencies are nearly equal for all categories, there may be no association between the variables. Such variables are said to be independent.

For the given conditional relative freduency, we can see that there is a significant difference between the columns of the table.
i.e. 0.15 is significantly different from 0.55 and 0.85 is significantly different from 0.45

Therefore, we can conclude from the given answer options that there is an association because the value 0.15 is not similar to the value 0.55