Question

leon is interested in the relationships among geographic region and political affiliation. leon collected data about the political parties of us senators at that time and the regions of the us that they represent. his results are in the table below.
region democrats republicans independents total
southeast 6 20 0 26
southwest 1 5 0 6
west 8 10 0 18
midwest 13 11 0 24
northeast 14 7 1 22
pacific 2 2 0 4
total 44 55 1 100
give the conditional distribution of political party for the northeast region. round your answers to the nearest tenth of a percent.

Explanation:

Step1: Recall conditional - distribution formula

The conditional distribution of a category within a subgroup is calculated as $\frac{\text{Frequency of the category in subgroup}}{\text{Total frequency of the subgroup}}\times100\%$.

Step2: Calculate proportion for Democrats in Northeast

For Democrats in the Northeast, the frequency is 14 and the total for the Northeast is 22. The proportion is $\frac{14}{22}\times100\%\approx63.6\%$.

Step3: Calculate proportion for Republicans in Northeast

For Republicans in the Northeast, the frequency is 7 and the total for the Northeast is 22. The proportion is $\frac{7}{22}\times100\%\approx31.8\%$.

Step4: Calculate proportion for Independents in Northeast

For Independents in the Northeast, the frequency is 1 and the total for the Northeast is 22. The proportion is $\frac{1}{22}\times100\%\approx4.5\%$.

Answer:

Democrats: 63.6%, Republicans: 31.8%, Independents: 4.5%