What Is The Population Under Consideration? What Are The Two

What Is The Population Under Consideration What Are The Two Variab

What is the population under consideration? What are the two variables under consideration? Group the bivariate data for the variables “birth region” and “party” into a contingency table. Count of Party Column Labels Row Labels D DR F R U W (blank) Grand Total MW NE SO WE (blank) Grand Total. Find the conditional distributions of birth region by party and the marginal distribution of birth region. Find the conditional distributions of party by birth region and the marginal distribution of the party. Does an association exist between the variables “birth region” and “party” for the U.S. presidents? Explain your answer. What percentage of presidents are Republicans? If no association existed between birth region and party, what percentage of presidents born in the South would be Republicans? In reality, what percentage of presidents born in the South are Republicans?

Paper For Above instruction

The analysis of the relationship between the birth region of U.S. presidents and their political party involves examining whether these two variables are associated or independent. To address this, it is essential to first define the population under consideration. Here, the population comprises all U.S. presidents, and the data pertains to their birth regions and political affiliations. The two key variables are "birth region" and "party," which are categorical and form the basis of a contingency table analysis.

The data can be organized into a contingency table, where the rows represent different birth regions—such as the Midwest (MW), Northeast (NE), South (SO), West (WE)—and the columns denote political party affiliations, including Democrat (D), Democrat-Republican (DR), Republican (R), Unaligned (U), W (possibly a placeholder or other), and blank categories representing missing or unknown data. Each cell within this table contains the count of presidents from a specific birth region and party, with marginal totals summing the counts across rows and columns.

Calculating the conditional distributions of birth region given party involves dividing the number of presidents from each birth region for a particular party by the total number of presidents belonging to that party. Conversely, the conditional distributions of party given birth region are obtained by dividing the number of presidents from each party within a specific birth region by the total number of presidents born in that region. These distributions reveal the likelihood of a president having a certain birth region given their party, and vice versa, which helps assess whether the variables are independent or associated.

The marginal distributions provide the overall proportion of presidents from each birth region and each party, regardless of any association. These are obtained by dividing the marginal totals by the grand total. Analyzing these distributions allows us to understand the prevalence of certain regions and parties among presidents overall.

To determine whether an association exists between birth region and party, a statistical test such as the Chi-Square Test of Independence would be used. A significant result indicates that birth region and party are associated, meaning that the distribution of one variable depends on the other. If the test suggests no association, the variables are considered independent, implying that the party affiliation of a president does not depend on their birth region.

Specific percentages of interest include the proportion of presidents who are Republicans, calculated by dividing the number of Republican presidents by the total number of presidents. Moreover, if no association existed between birth region and party, we would expect the percentage of presidents born in the South who are Republicans to be approximately equal to the overall percentage of Republicans among all presidents. In practice, however, the actual percentage might differ, indicating a possible association between being born in the South and Republican party affiliation among presidents.

In conclusion, analyzing the contingency table and the associated distributions offers insights into the relationship between birth region and party among U.S. presidents. Such an analysis helps uncover patterns and whether regional origins influence political alignment, enriching our understanding of political demographics over American history.

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