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Question 6 of 23
Some defendants in criminal proceedings plead guilty and are
sentenced without a trial, whereas others who plead innocent are
subsequently found guilty and then are sentenced. In recent years,
legal scholars have speculated as to whether sentences of those who
plead guilty differ in severity from sentences for those who plead
innocent and are subsequently judged guilty. Consider the data given
below on defendants accused of robbery, all of whom, by the way,
had previous prison records. At the .01 level of significance, do these
data suggest that the proportion of all defendants in these
circumstances who plead guilty and are sent to prison differs from the
proportion who are sent to prison after pleading innocent and being
found guilty?
Plea
Guilty
Not Guilty
Number judged guilty
n1 = 191
n2 = 64
Number sentenced to prison
x1 = 101
x2 = 56
Sample proportion
.529
.875
A.No, because the test value -1.96 is inside the interval (-2.58, 2.58)
B.No, because the test value -4.94 is outside the interval (-1.96, 1.96)
C.Yes, because the test value 2.58 is inside the interval (-4.94, 4.94)