Hypothesis Testing: Comparing Means and Proportions in Criminology, Assignments of Criminology

Download Hypothesis Testing: Comparing Means and Proportions in Criminology and more Assignments Criminology in PDF only on Docsity! CCJS 200 - Fall 20X6 - Ilomework 10 - Hypothesis Testing with 2 Means or Proportions Directions: Please answer all questions on another sheet of paper. Place your name on all sheets and staple all sheets together. REMINDER: Write the following honor pledge on your homework and sign: I pledge on my honor that I have not given nor received any unauthorized qssistance on this assignment 1. Some criminologists argue there is a relationship between "impulsivity" and criminal offending. The idea is that impulsive people act on immediate gratification and that since crime involves quick pleasure and only the long-term possibility of any cost (getting caught and punished), it should be highly attractive to them. To test this notion you take a random sample of 120 people, you give them a personality test that includes a measure of impulsivity. Based on this test, you divide your sample into two groups: (l) the non-impulsive group @:8Q)and, (2) the impulsive group (rl-40): You then ask each person to report the number of criminal offenses they have committed in the last year. Finally, you calculate the mean number of self-reported offenses for each group, and here is the data you get: Impulsive (n1 :40) X1:13.5 s1 :4.9 Non-Impulsive Gz: 80) Xz:10.3 s2:4'0 .nOr- .f a). Test the null hypothesis that there is tpl!!ffefegAg between the two grcups versus the altegqtivqhypothesis that those who are impulsive commit more criminal offenses. Use anl@lp[A.of.Oland label each step of your hypothesis test. Assume that the two population standard deviations are equal (or:oz), and make sure to properly interpret your results. j,.*t'.tt"\' 'l 2. The following data show the number of unsafe needles used per week for a group of 7 heroin users before and after an AIDS education program. Theisamplemean',number oTunsafe needles before the program is 1.71 needles and the sample mean number of unsafe needles after the program is 1.29. The standard deviation in each case is 0.75. Test the null hypothesis that the mean number of unsafe needles used after the education program is the same as the mean number before the program against the alternative that the mean number of unsafe needles after the program is less than the mean number before the program. Use an alpha of 0.05 and interpret 1', !l a +.1 your results. Person I 2 3 4 5 6 7 Before ) a J After 2 2 2 0 I 1 1 I 2 I 2 I )r- 3. It has been argued that capital punishment decreases the homicide rate. If this is true, jurisdictions with the death penalty should have lower homicide rates than jurisdiction will life imprisonment. To test this assertion, you take a sample of 28 states that have the death penalty on the books and have used it in the past five years (call them "death" states) and find that they have an average homicide rate of 25.3 per 100,000 with a standard deviation of 7.0. You take a second independenl sample of 14 states that do not have the death penalty (call them *life'o states) and find that they have a mean homicide rute of 24.8 per 100,000 with a standard deviation of 7.5. You also know that the population variances are not equal to one another (orfoz). a) What is the independent variable and what is the dependent variable in this question? b) Test the null hypothesis that the mean homicide rate for death and life states is the same, against the altetnative that it is different. Use an alpha of .01 with 30 degrees of freedom and state each step of your hypothesis test. Be sure to state your conclusion about the deterrent effect of capital punishment. nd ,51 4. In many states, ex-offenders are disenfranchised, meaning that they cannot vote. After a long political campaign in one state, ex-offenders have been re-enfranchised, meaning that they can now vote after serving their sentence and remaining unarrested for 2 years. The state Democratic Party thinks that many of these voters will vote for the Democratic candidate, but is *onied that they will exercise their right to vote at a different rate than the general population. To test this idea, they authorize a survey in which they ask people whether or not they intend to vote. The survey takes two random independent samples, one of 125 ex-offenders who quafiry to vote, and one of 130 non-offenders. The samples are representative of the entire ex-offender population and the general non-offender population in the state. The survey finds that 57 of the 130 non- offenders intend to vote and 75 of the 125 ex-offenders intend to vote. l?6 x, IJP N,^