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Chapter 10: Problem 27

Suppose a polling organization asks a random sample of people if they are Democrat, Republican, or Other and asks them if they think the country is headed in the right direction or the wrong direction. If we wanted to test whether party affiliation and answer to the question were associated, would this be a test of homogeneity or a test of independence? Explain.

Short Answer

Expert verified
The scenario described in this exercise represents a test of independence.

Step by step solution

01

Understanding the Concepts

The first step is to understand the underlying statistical concepts. A test of independence checks if the distribution of a categorical variable (here, the opinion on the country's direction) depends on another categorical variable (here, the party affiliation). In simpler terms, it checks if the two variables are interconnected or influence each other; in this case, whether a person's political party affiliation influences their opinion about the country's direction. On the other hand, a Test of Homogeneity evaluates if multiple populations (a group or set of entities) have the same proportions for a categorical response - it is used when data is gathered from different populations to see if they function the same way.
02

Identifying the Test Type in the Scenario

Looking at the given scenario, the polling organization poses a question on party affiliation - Democrat, Republican, or Other - and then asks the same sample of people about their opinion on the country's direction. Therefore, the purpose here is not to compare different populations, but rather to see if these two categorical variables from the same population are associated - i.e., if one's party affiliation affects their opinion on the country's direction.
03

Conclusion

Given that the exercise is trying to understand whether there is an association between party affiliation and opinion on the country's direction within the same population, it is a test of independence. It seeks to identify if knowing a person's party affiliation can help predict their opinion about the country's direction. It is not a matter of comparing different populations (as in a Test of Homogeneity), but rather understanding the relationship within a single population.

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