A One-Tailed Test With Unequal Population Variances: Trial Types and Sentence Lengths
For the second t -test example, we will again use the JDCC data on juveniles diverted to adult criminal courts. Let’s consider whether the length of time it takes for a juvenile’s case to be disposed of is affected by the type of attorney the juvenile has. The prediction will be that juvenile defendants who retain private counsel experience significantly longer time-to-disposition compared to those who use the services of public defenders. This, theoretically, is because private attorneys might file more pretrial motions and spend more time negotiating with the prosecutor and the judge. The sample is narrowed to juveniles charged with violent offenses who were not released pending trial and who were ultimately sentenced to prison. Those with private attorneys (N = 36) had a mean of 7.93 months to disposition (s = 4.53), whereas those represented by public defenders (N = 234) experienced a mean of 6.36 months (s = 3.66). We will call the defendants who retained private attorneys Sample 1 and those who were represented by public defenders Sample 2. Using an alpha level of .01 and the assumption that the population variances are unequal, we will conduct a five-step hypothesis test to determine whether persons convicted by juries receive significantly longer prison sentences.
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