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.

A 4-column table with 3 rows titled number of calories and location of meal preparation. The first column has no label with entries greater than or equal to 500 calories, less than 500 calories, total. The second column is labeled home with entries 0.15, 0.85,1.0. The third column is labeled restaurant with entries 0.55, 0.45, 1.0. The fourth column is labeled total with entries 0.28, 0.72, 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.

Answer 1

B

Explanation:

Answer 2

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

For the nutritionist to determine whether there is an association between where food is prepared and the number of calories the food contains, there must be an association between two categorical variables.

The conditions that satisfy whether there exists an association between conditional relative frequencies are:

1. When there is a bigger difference in the conditional relative frequencies, the stronger the association between the variables.

2. When the conditional relative frequencies are nearly equal for all categories, there may be no association between the variables.

For the given conditional relative frequency, we can see that there exists a significant difference between the columns of the table in the picture because 0.15 is significantly different from 0.55 and 0.85 is significantly different from 0.45

We can conclude that there is an association because the value 0.15 is not similar to the value 0.55