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Chapter 10: Problem 29

A 2018 Gallup poll asked college graduates if they agreed that the courses they took in college were relevant to their work and daily lives. The respondents were also classified by their field of study. If we wanted to test whether there was an association between response to the question and the field of study of the respondent, should we do a test of independence or homogeneity?

Short Answer

Expert verified
A test of independence should be performed.

Step by step solution

01

Understand the Definitions

A test of independence is used to determine if there is a significant relationship between two categorical variables in a sample. It is used when data is collected from a single group. A test of homogeneity, on the other hand, is used to decide whether different populations or groups have the same distribution of a single categorical variable.
02

Apply the Definitions to the Problem

Looking at our problem, we have two categorical variables: the respondent's answer (yes or no) and their field of study. The data comes from one group - college graduates. Therefore, we're looking for a relationship between two categorical variables from a single group.
03

Determine the Appropriate Test

Given these circumstances, we should use a test of independence. This test will allow us to establish whether there's a significant association between the field of study of the respondents and their response to the question.

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Most popular questions from this chapter

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.

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According to the website MedicalNewsToday.com, coronary artery disease accounts for about \(40 \%\) of deaths in the United States. Many people believe this is due to modern-day factors such as high-calorie fast food and lack of exercise. However, a study published in the Journal of the American Medical Association in November 2009 (www.medicalnewstoday .com) reported on 16 mummies from the Egyptian National Museum of Antiquities in Cairo. The mummies were examined, and 9 of them had hardening of the arteries, which seems to suggest that hardening of the arteries is not a new problem. a. Calculate the expected number of mummies with artery disease (assuming the rate is the same as in the modern day). Then calculate the expected number of mummies without artery disease (the rest). b. Calculate the observed value of the chi-square statistic for these mummies.
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