Question

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

Part (b): Determine the conditional distribution of political party affiliation within each class level.

Part (c): Are the variables "political party affiliation" and "class level" for this population of night-school students associated? Explain your answer.

Part (d): Without doing any further calculation, determine the marginal distribution of political party affiliation?.

Part (e): Without doing further calculation, respond true or false to the following statement and explain your answer: "The conditional distributions of class level within political party affiliations are distributions of class level within political party affiliations are identical to each other and to the marginal distribution of class level."

Short answer

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

Part (b): The distribution is given below,

Part (c): No association between the two given variables. As the table in part (b) shows the conditional distributions of political party affiliation within class level are identical.

Part (d): The marginal distribution of political affiliation is republican $0.5$, democrat $0.333$and other $0.167$.

Part (e): True as from part (c), it is known that the two variables "class level" and "political affiliation" are not associated.

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 "political party affiliation" 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,

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

No, the variables "political party affiliation" and "class level" for this population of night-school students doesn't associate.

The table in part (b) shows the conditional distributions of political party affiliation within class level are identical.

Part (d) Step 1. Determine the marginal distribution.

Without any calculation, the marginal distribution of political affiliation is given below,

As there is no association between the two given variables.

Part (e) Step 1. Explain if the statement is true or false.

The statement is true.

As from part (c), it is known that the two variables "class level" and "political affiliation" are not associated.