A researcher is hired to investigate the effects of a drug treatment program on subsequent recidivism of drug offenders. Recidivism is measured by a urinalysis that will yield evidence of positive or negative drug use. The researcher observes that those individuals completing an 8 week version of the program have significantly higher levels of recidivism than those individuals who were assigned to a 12 week version of the program. The researcher concludes that the four extra weeks resulted in the lower recidivism rates. Do you agree or disagree with the researchers conclusion? Why did you make the choice that you did?
Added by Richard R.
Step 1
Step 1: The researcher observed that individuals completing an 8 week version of the program had higher levels of recidivism compared to those completing a 12 week version. Show more…
Show all steps
Close
Your feedback will help us improve your experience
Ameer Said and 84 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
A study of the post treatment behavior of a large number of drug abusers suggests that the likelihood of conviction within a two-year period after treatment may depend upon the offenders education. The proportions of the total number of cases falling in four education-conviction categories are shown in the following table. Status within 2 Years after Treatment Education Convicted Not Convicted Total 10 years or more 0.20 0.10 0.30 9 years or less 0.11 0.59 0.70 Total 0.31 0.69 1.00 Suppose that a single offender is selected from the treatment program. Define the following events. A: The offender has 10 or more years of education. B: The offender is convicted within two years after completion of treatment. (a) Find P(A). (b) Find P(B). (c) Find P(A ∩ B). (d) Find P(A ∪ B). (e) Find P(A). (f) Find P(A ∪ B). (g) Find P(A ∩ B). (h) Find P(A|B). (Round your answer to two decimal places.) (i) Find P(B|A). (Round your answer to two decimal places.)
Kari H.
In the Scientific American article "Reducing Crime: Rehabilitation is Making a Comeback," R. Doyle examined rehabilitation of felons. One aspect of the article discussed recidivism of juvenile prisoners between 14 and 17 years old, indicating that $82 \%$ of those released in 1994 were rearrested within 3 years. Suppose that, today, six newly released juvenile prisoners between 14 and 17 years old are selected at random. a. Assuming that the recidivism rate is the same today as it was in 1994, determine the probability distribution for the number, $Y,$ who are rearrested within 3 years. b. Determine and interpret the mean of $Y$. c. If, in fact, exactly two of the six newly released juvenile prisoners are rearrested within 3 years, would you be inclined to conclude that the recidivism rate today has decreased from the $82 \%$ rate in 1994? Explain your reasoning. Hint: First consider the probability $P(Y \leq 2).$ d. If, in fact, exactly four of the six newly released juvenile prisoners are rearrested within 3 years, would you be inclined to conclude that the recidivism rate today has decreased from the $82 \%$ rate in 1994? Explain your reasoning.
Discrete Random Variables
The Binomial Distribution
Harsh, mandatory minimum sentences for drug offenses account for more than half the population in U.S. federal prisons. The bar graph shows the number of inmates in federal prisons, in thousands, for drug offenses and all other crimes in 1998 and 2010. (Other crimes include murder, robbery, fraud, burglary, weapons offenses, immigration offenses, racketeering, and perjury.) a. In 1998, there were 60 thousand inmates in federal prisons for drug offenses. For the period shown by the graph, this number increased by approximately 2.8 thousand inmates per year. Write a function that models the number of inmates, y, in thousands, for drug offenses x years after 1998. b. In 1998, there were 44 thousand inmates in federal prisons for all crimes other than drug offenses. For the period shown by the graph, this number increased by approximately 3.8 thousand inmates per year. Write a function that models the number of inmates, y, in thousands, for all crimes other than drug offenses x years after 1998. c. Use the models from parts (a) and (b) to determine in which year the number of federal inmates for drug offenses was the same as the number of federal inmates for all other crimes. How many inmates were there for drug offenses and for all other crimes in that year?
Systems of Equations and Inequalities
Systems of Linear Equations in Two Variables
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD