Sampling and Hypothesis Data - Report Example

Sampling and Hypothesis Data This report contains the results of a hypothesis test conducted on legal service and sentence satisfaction scores. The analysis used the data captured in the survey conducted on inmates in United States of America. The study participants awarded scores to each service based on their satisfaction level. The calculated mean scores of legal services and sentence satisfaction were 5.232 and 4.952 respectively. Another, statistic calculated was the variance for the two variables. The calculated t-value (0.947866357) was less than the critical value (2.063898562). Therefore, the null hypothesis failed rejection. Consequently, the t test analysis established that there was no statistically significance difference between the mean of legal satisfaction and sentence satisfaction. Introduction Legal representation and the sentence conformity to the constitutional requirement are key factors, which influence the perception of fairness in the criminal justice system. It is for this reasons that most progressive constitutions contain provisions outlining the rights of the accused. These constitutions use the presumption of innocence until proven guilty principle to advance these rights with a view of promoting fair judicial process for all. In United States, the Sentencing Commission is the authority charged with the responsibly of developing sentencing guidelines and policies for federal court system (Finley, 2011). While, there is one agency responsible for this task at national level, different state agencies formulate sentencing policies at state levels. This brings a situation whereby same offence does not attract uniform punishment in US. Consequently, the jurisdiction influences the level of satisfaction with the sentence delivered by judges. On legal representation front, the government established a Legal Services Corporation in 1974 to boost access to legal service to poor Americans (National Emergency Council, 2011). However, the legal aid only benefits few applicants with civil cases. Meaning, the Americans facing criminal charges do not gent legal grants. This discrimination on the offence basis makes it hard for low-income earners to get legal services aid. However, the Constitution of US prohibits the denial of a person similar treatment given to other persons in the legal system. Analysis and Discussion 1. Student t test is a parametric hypothesis test that evaluates whether the mean of variables have statistically significance variation. In this case, the mean scores for legal service and sentence satisfaction are at the center of this determination. The analysis begins with the statement of null and alternative hypothesis. The null hypothesis assumes that the means have no statistically significant difference while the alternative hypothesis assumes otherwise. Then, the setting of criterion for rejection of hypothesis follows statements of hypothesis. This stage involved the definition of the rejection region by first fixing the significance level at 0.05. Thereafter, a computation of the test statistic follows. Then, the decision on whether to reject the null hypothesis based on calculated and critical t-value takes the final step. 2 2. H0: There is no statistically significant difference between the mean of Legal Service and the mean of Sentence Satisfaction M1 = M2 H1: There is a statistically significant difference between the mean of Legal Service and the mean of Sentence Satisfaction M1 ≠ M2 3. Sample Mean 1 (M1) = 130.8/25 = 5.232 Sample Mean 2 (M2) =123.8/25 = 4.952 Sample Variance 1(Var1) =1.0306 Sample Variance 2 (Var2) =1.150933333 Degree of freedom (n1+n2) -2 =48 Test-statistic = M1 –M2 / Sqrt {(var1÷ n1) + (var2 ÷ n2)} 5.232 - 4.952/Sqrt {(1.0306÷25) + (1.15093÷25)} 0.947866357 4. t-Test: Two-Sample Assuming Unequal Variances   Variable 1 Variable 2 Mean 5.232 4.952 Variance 1.0306 1.150933333 Observations 25 25 Hypothesized Mean Difference 0 df 48 t Stat 0.947866357 P(T Read More