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?
Guilty Not Guilty
Number judged guilty n1 = 191 n2 = 64
Number sentenced to prison x1 = 101 x2 = 56
Sample proportion P1 = .529 p2 = .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 -4.94 is outside the interval (-2.58, 2.58)
D. Yes, because the test value 2.58 is inside the interval (-4.94, 4.94)
The solution provides step by step method for the calculation of confidence interval for two proportions . Formula for the calculation and Interpretations of the results are also included.