There are three major objectives of this homework 1To contin

There are three major objectives of this homework:

1.To continue becoming familiar with Markdown.

2.To learn how to use the R-packages and boot to compute confidence intervals.

3.To interpret such confidence intervals and use them to assess the quality of your point estimates.

The points to this homework are distributed as follows:

Requirement

Points

Professionalism

20

R Markdown

10

1. Recidivism

35

2. Yellowstone

35

Total

100

Q1. Recidivism

Recidivism is one of the most fundamental concepts in criminal justice. It refers to a person\'s relapse into criminal behavior, often after the person receives sanctions or undergoes intervention for a previous crime. Recidivism is measured by criminal acts that resulted in rearrest, re-conviction or return to prison with or without a new sentence during a three-year period following the prisoner\'s release.

Bureau of Justice Statistics studies have found high rates of recidivism among released prisoners. One study tracked 404,638 prisoners in 30 states after their release from prison in 2005. The researchers found that:

Within three years of release, about two-thirds (67.8 percent) of released prisoners were rearrested.

•Within five years of release, about three-quarters (76.6 percent) of released prisoners were rearrested.

•Of those prisoners who were rearrested, more than half (56.7 percent) were arrested by the end of the first year.

•Property offenders were the most likely to be rearrested, with 82.1 percent of released property offenders arrested for a new crime compared with 76.9 percent of drug offenders, 73.6 percent of public order offenders and 71.3 percent of violent offenders.

Q1.1 Point estimate

What is the point estimate of the proportion that are arrested within 3 years?

Q1.2 Create synthetic sample

Create a synthetic sample using the size of 404,638 where 67.8% of the released prisoners are coded with a 1 and the rest are coded as 0.

1.3 Create a bootstrap sampling distribution

Create a bootstrap sampling distribution by bootstrapping the sample using 1000 replications. Note that this will take some time. How long will depend upon the age of your computer. It should take under 10 minutes. I have a new computer and it took about 30 seconds.

1.4 Assess the shape of the sampling distribution

Use the package to draw a histogram of the bootstrap sampling distribution. Give an assessment of the sampling distribution.

1.5 Point estimates and bias evaluation.

•What is the point estimate of the proportion of released prisoners who are re-arrested within after release?

•What is the bootstrap sampling bias and the absolute percentage bias? Do you need to increase the number of bootstrap replications? If so increase the number of replications.

1.6 Confidence interval

Select the appropriate bootstrap confidence interval. Then compute the interval. Round the interval to three decimal places. Use a 99% level of significance.

1.7 Interpretation of the confidence interval and analysis.

Give the point estimate value of the proportion, and the 99% confidence bounds. Write this in a short paragraph. Discuss the quality of the estimate.

Solution