Testing of Hypothesis

Question One. Data from the National Youth Survey on the number of assaults on students appears to indicate some gender differences. State the null and alternate hypotheses to test this theory, choose the appropriate test statistic and variance estimator and justify their choice, determine the critical value for the test statistic at an alpha level of 0.01 (one-tailed), and state your conclusion.
Males: Females:
N = 912 N = 802
mean = 8.64 mean = 1.79
SD = 48.39 SD = 9.16

Question Two. As a condition of their parole, individuals must participate in anger management therapy and make satisfactory progress. The practice has recently come under attack by local political groups who claim that the therapy is not making any difference. Your supervisor has asked you to analyze data from a small sample of parolees to determine if the therapy is having the desired impact. Below are the pre and post test data for an anger management scale for fifteen parolees. On this scale, high scores indicate more anger. State your null and alternate hypotheses, decide what type of test would best be suited to analyze these data, choose the critical value for the test statistic and state your conclusion. Use an alpha of 0.01.
Subject Score Before Score After
1 32 21
2 31 20
3 21 9
4 48 21
5 18 19
6 21 19
7 32 20
8 35 14

9 41 12
10 42 10
11 40 9
12 38 30
13 22 21
14 35 30
15 37 31

Question Three. A researcher has information from large samples of both males and females on the number of self-reported delinquent acts. She wants to determine the 95% confidence interval for each of these estimates for each of these estimates so she will ahve a better idea of the range of likely values for these samples. Use the data below to calculate the 95% confidence intervals for these mean values.
Males: Females:
N = 12003 N = 12226
mean = 1.349 mean = 0.5357
SD = 1.6204 SD = 1.1008

Question Four. A drug treatment facility has a 42% successful completion rate. During the past cycle, 248 individuals were enrolled in the treatment facility. Calculate the 99% confidence interval for the success rate of this group at the treatment clinic.

Question Five. A researcher is interested in the differences in academic behavior of delinquents versus non-delinquents. He separates his sample into those who have reported delinquent acts and those who have not. Calculate the 95% confidence interval for the difference between means. Use the separate variance method.
Non-delinquent: Delinquent:
N = 14197 N = 10032
GPA = 3.159 GPA = 2.759
= 0.8427 = 1.329