4.7. Chi-Square Tests 291
Table 4.7.1:Contingency Table for Type of Crime and Alcoholic Status Data
Crime Alcoholic Non-Alcoholic
Arson 50 43
Rape 88 62
Violence 155 110
Theft 379 300
Coining 18 14
Fraud 63 144that the two distributions are the same (and hence the two teaching procedures are
equally effective). For computation in R, use
r1=c(15,25,32,17,11);r2=c(9,18,29,28,16);mat=rbind(r1,r2)
chisq.test(mat)
4.7.7.Kloke and McKean (2014) present a data set concerning crime and alco-
holism. The data they discuss is in Table 4.7.1. It contains the frequencies of
criminals who committed certain crimes and whether or not they are alcoholics.
The data are also in the filecrimealk.rda.
(a)Using code similar to that given in Exercise 4.7.6, compute theχ^2 -test for
independence between type of crime and alcoholic status. Conclude in terms
of the problem, using thep-value.(b)Use the Pearson residuals to determine which part of the table contains the
strongest information concerning dependence.(c)Use aχ^2 -test to confirm your suspicions in Part (b). This is a conditional test
based on the data, but, in practice, such tests are used for planning future
studies.4.7.8.Let the result of a random experiment be classified as one of the mutually
exclusive and exhaustive waysA 1 ,A 2 ,A 3 and also as one of the mutually exhaustive
waysB 1 ,B 2 ,B 3 ,B 4. Say that 180 independent trials of the experiment result in
the following frequencies:
B 1 B 2 B 3 B 4
A 1 15 − 3 k 15 −k 15 +k 15 + 3k
A 2 15 15 15 15
A 3 15 + 3k 15 +k 15 −k 15 − 3 kwherekis one of the integers 0, 1 , 2 , 3 , 4 ,5. What is the smallest value ofkthat
leads to the rejection of the independence of theAattribute and theBattribute at
theα=0.05 significance level?
4.7.9.It is proposed to fit the Poisson distribution to the following data: