Question

Consider the variables "gender" and "college".

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

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

Part (c): Determine the conditional distribution of college within each college and the marginal distribution of college.

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

Short answer

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

Part (b): The distribution is given below,

Part (c): The distribution is given below,

Part (d): Yes. As the conditional distributions of one variables given the other are not identical.

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 "college" 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 college.

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

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 "college" for this population.

Because the conditional distributions of one variables given the other are not identical.