1. A researcher is interested in whether gender affects the probability of being arrested. They gather a random sample

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1.  A
researcher is interested in whether gender affects the probability
of being arrested. They gather a random sample of 3996 women and
find that 801 of them have been arrested. This compares to 1808 men
arrested from a random sample of 4155 men.
2. The researcher
also believes that ethnicity might affect the probability of arrest
and obtains the following data
Black
Hispanic
non-black/non-Hispanic
mixed race/non-Hispanic
number arrested
794
534
29
1252
number not arrested
1384
1210
49
2899
a) Is the probability
of being arrested independent of ethnicity? [10
marks]
b) How would we go
about testing whether a particular ethnic group is different from
the others? [5 marks]
c) How would we test
whether the probability of being arrested is affected independently
by both gender and ethnicity? What about testing for whether the
effect of gender is different for different ethnic groups?
[10 marks]
d) Why might this
analysis give us the wrong answer about the relationship between
ethnicity, gender and the probability of arrest? [5
marks]