A group of social psychologists studying the effects of power and wealth on people’s behavior…

A group of
social psychologists studying the effects of power and wealth on people’s
behavior examined the relationship between the status, or prestige, of vehicles
approaching four-way stops and the likelihood that the approaching vehicle
would cut off other vehicles that were already stopped at the intersection.
They grouped approaching vehicles into five status categories (1 = lowest to 5
= highest), according to the vehicle’s make, age, and physical appearance. They
also recorded whether each approaching vehicle cut off other vehicles. In the
sample of 282 approaching vehicles, 41 were
»

A group of
social psychologists studying the effects of power and wealth on people’s
behavior examined the relationship between the status, or prestige, of vehicles
approaching four-way stops and the likelihood that the approaching vehicle
would cut off other vehicles that were already stopped at the intersection.
They grouped approaching vehicles into five status categories (1 = lowest to 5
= highest), according to the vehicle’s make, age, and physical appearance. They
also recorded whether each approaching vehicle cut off other vehicles. In the
sample of 282 approaching vehicles, 41 were in category 1, 46 in category 2,
110 in category 3, 50 in category 4, and 35 in category 5.

a. Imagine
that one of the members of the research team wants to test the idea that there
is no relationship between a vehicle’s status and the likelihood that it will
cut off other vehicles. What kind of chi-square test should the researcher set
up: a test of independence or goodness-of-fit? Give the and alternative
hypotheses for the appropriate test.

b. Say
that another member of the research team wants to test the idea that
approaching vehicles will cut off other cars at the same rates that people from
different income quintiles are known to cut off others in conversation from
past research. For example, since past research indicates that people in the
highest income quintile cut off others in conversation 37% of the time, the
prediction would be that the highest status vehicles (category 5) would cut off
other vehicles 37% of the time. On average, people from other income quintiles
have been found to cut off others in conversation as follows: Quintile 1: 8%,
Quintile 2: 15%, Quintile 3: 20%, and Quintile 4: 28%. What kind of chi-square
test should the researcher set up: a test of independence or goodness-of-fit?
Give the and alternative hypotheses for the test.

c. Figure
12.12 shows the expected frequencies for each group from the chi-square test
for either Part a or b. With which chi-square test do these expected
frequencies correspond? How can you tell?

d. The
sample chi-square from the test for Part c is found to be statistically
significant at the 0.05 alpha-level. The researcher concludes that there is no
relationship between vehicle status and cutting off other vehicles. Is this
conclusion accurate? If yes, explain why. If no, give an accurate conclusion.

e. Based
on the expected frequencies shown in Figure 12.12, would you recommend that the
analysis proceed? Explain your recommendation.

 

»

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