Question

In: Statistics and Probability

1. A criminologist is interested in whether there was any disparity in sentencing based on the...

1. A criminologist is interested in whether there was any disparity in sentencing based on the race of the defendant. She selected two random samples of burglary convictions in one jurisdiction and recorded the prison terms given to the 10 white defendants in one sample and the 8 black defendants in the other sample. The sentence lengths (in years) for individuals in the two groups are shown below, along with the sample means and standard deviations. Using these data and a 0.05 alpha level, test the hypothesis that white and black defendants convicted of burglary in this jurisdiction receive prison sentences of different length.

White Defendants Black Defendants
3 4
5 8
4 7
7 3
4 5
5 4
6 5
4 4
3
2

a. In symbols and words, what is the null hypothesis for this test?

b. In symbols and words, what is the alternative hypothesis for this test?

c. Is this a one-sided or two-sided test? How do you know?

d. Will you use a z-test or a t-test in this situation? Why?

e. What is the critical value of the test statistic?

f. What is the value of the test statistic calculated from the sample results?

g. What decision about the null hypothesis does your test lead to?

h. Is the observed racial difference in sentence length statistically significant? Explain.

i. Would your decision be different if you used an alpha level of .01? Explain.

Solutions

Expert Solution

Answer question


Related Solutions

Dr. Roh was interested in whether there was any disparity in sentencing based on the race...
Dr. Roh was interested in whether there was any disparity in sentencing based on the race of the defendant. He selected at random 19 drug convictions for cocaine distribution and completed the prison terms given to the 10 whites and 10 blacks sampled. The sentence lengths (in years) are shown below for the white and black offenders White Black 3 4 5 8 2 7 7 7 4 5 5 9 5 7 4 4 3 5 2 8 FYI,...
A criminologist is interested in the effects of unemployment and policing on murder and has run...
A criminologist is interested in the effects of unemployment and policing on murder and has run the following multiple regression: Summary Output Regression Statistics Multiple R 0.90303 R Square 0.815462 Adjusted R Square 0.762737 Standard Error 5.11041 Observations 10 Coefficients Standard Error t Statistic P-value Intercept –23.26309588 7.075518018 –3.28783 0.013342 Unemployment rate 10.27754326 2.172859937 4.729961 0.002133 Police per 100,000 –0.046737101 0.023409765 –1.99648 0.086065 a. What is the Y-intercept? Interpret your results. b. Which variables are significant at the 0.05 level?...
A criminologist is interested in possible disparities in the length of prison sentences between males and...
A criminologist is interested in possible disparities in the length of prison sentences between males and females convicted in murder-for-hire cases. Selecting 14 cases involving men convicted of trying to solicit someone to kill their wives and 16 cases involving women convicted of women trying to solicit someone to kill their husbands, the criminologist finds the following: For males, the mean length of the prison sentences is M = 7.34 with SS = 82 For females, the mean length of...
As a criminologist, you are interested in the factors related to juvenile offending. You think that...
As a criminologist, you are interested in the factors related to juvenile offending. You think that time spent studying influences delinquent behavior. In a group of 21 high school students, you collect information about the number of times a juvenile has broken curfew this month and how much time they spend studying this month. You break the sample into three groups, those who spend no time studying, those who spend less than 1 hour per day, and those who spend...
A researcher is interested in whether or not there is a difference in student’s performance based...
A researcher is interested in whether or not there is a difference in student’s performance based on the study methods they use. Participants are assigned one of three different study methods (read the text and re-read it, read and answer prepared questions, and read then create your own questions). There are 6 people in each group and the researcher measures the participants’ performance on a test. Perform a hypothesis test and show all four steps. Hints: Use a two tailed...
Two college instructors are interested in whether or not there is any variation in the way...
Two college instructors are interested in whether or not there is any variation in the way they grade math exams. They each grade the same set of 12 exams. The first instructor's grades have a variance of 52.3. The second instructor's grades have a variance of 89.9. Test the claim that the first instructor's variance is smaller. The level of significance is 5%.
Two college instructors are interested in whether or not there is any variation in the way...
Two college instructors are interested in whether or not there is any variation in the way they grade math exams. They each grade the same set of 12 exams. The first instructor's grades have a variance of 52.3. The second instructor's grades have a variance of 89.9. Test the claim that the first instructor's variance is smaller. The level of significance is 5%.
College students may be interested in whether or not their majors have any effect on starting...
College students may be interested in whether or not their majors have any effect on starting salaries after graduation. Suppose that 295 recent graduates were surveyed as to their majors in college and their starting salaries after graduation. Below are the data. Conduct a test of independence. (Use a significance level of 0.05.) Major < $50,000 $50,000 - $68,999 $69,000 + English 4 20 6 Engineering 9 29 59 Nursing 10 16 14 Business 11 19 30 Psychology 20 29...
Short Answer 6 You are interested in whether the virus impacts any part of a cell’s...
Short Answer 6 You are interested in whether the virus impacts any part of a cell’s cytoskeleton. What are three experiments you would carry out to study this? Be specific with the different cytoskeletal components
Q1. Researchers were interested in determining whether there were any differences in the tendency to procrastinate...
Q1. Researchers were interested in determining whether there were any differences in the tendency to procrastinate based on birth order, i.e. first, second, or third child born. Using the data in the table below, answer the following questions. State the null and alternate hypotheses. What is the total sample size? Identify the independent and dependent variables What is the test statistic value? What is the p value? What is your conclusion (assume α = .05)? Phrase your conclusion based on...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT