Q1) Some defendants in criminal proceedings plead guilty and are sentenced without a trial, while others who plead innocent are subsequently found guilty and then are sentenced. In current years, legal scholars have speculated as to whether sentences of those who plead guilty vary in severity from sentences for those who plead innocent and are subsequently judged guilty. Let data given below on defendants accused of robbery, all of whom, by way, had previous prison records. At.01 level of significance, do these data suggest that proportion of all defendants in these situations who plead guilty and are sent to prison varies from proportion who are sent to prison after pleading innocent and being found guilty?
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Plea
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Guilty
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Not Guilty
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Number judged guilty
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n1 = 191
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n2 = 64
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Number sentenced to prison
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x1 = 101
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x2 = 56
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Sample proportion
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i) No, as the test value -1.96 is inside interval (-2.58, 2.58)
ii) No, as the test value -4.94 is outside interval (-1.96, 1.96)
iii) Yes, as the test value -4.94 is outside interval (-2.58, 2.58)
iv) Yes, as the test value 2.58 is inside interval (-4.94, 4.94)