Question

Consider the variables "gender" and "class level."

Part (a): Group the bivariate data for these two variables into a contingency table.

Part (b): Determine the conditional distribution of gender within each class level and the marginal distribution of gender.

Part (c): Determine the conditional distribution of class level within each gender and the marginal distribution of class level.

Part (d): Does an association exist between the variables "gender" and "class level" for this population? Explain your answer.

Short answer

Part (a): The contingency table is given below,

Part (b): The distribution is given below, where the last given row shows the marginal distribution of the variable gender,

Part (c): The distribution is given below, where the last column shows the required marginal distribution,

Part (d): Yes. If there was no association then the conditional distribution of class levels within the genders male and female would be identical, but this is not the case.

Step-by-step solution

Part (a) Step 1. Given information,

Consider the given question,

Part (a) Step 2. Write the contingency table. 

On grouping the bivariate data for the two variables "gender" and "class level" into a contingency table is given below,

Part (b) Step 1. Determine the conditional distribution of gender.

The table given below is of required conditional and marginal distribution,

The last given row shows the marginal distribution of the variable gender.

Part (c) Step 1. Determine the conditional distribution of class level.

The table given below is of required conditional and marginal distribution,

The column headed "F", shows the distribution of class level within females. Similarly, the column "M" shows the distribution within males.

Hence, the last column shows the required marginal distribution.

Part (d) Step 1. Explain if an association exist.

Yes, an association exist between the variables "gender" and "class level" for this population.

If there was no association then the conditional distribution of class levels within the genders male and female would be identical, but this is not the case.