/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 64 A study of the death penalty in ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Problem 64

A study of the death penalty in Kentucky reported the results shown in the table. (Source: Data from T. Keil and G. Vito, Amer. \(J .\) Criminal Justice, vol. \(20,1995,\) pp. \(17-36 .)\) a. Find and compare the percentage of white defendants with the percentage of black defendants who received the death penalty, when the victim was (i) white and (ii) black. b. In the analysis in part a, identify the response variable, explanatory variable, and control variable. c. Construct the summary \(2 \times 2\) table that ignores, rather than controls, victim's race. Compare the overall percentages of white defendants and black defendants who got the death penalty (ignoring, rather than controlling, victim's race). Compare to part a.

Short Answer

Expert verified
Calculate percentages with separate considerations for victim's race in Part a. Use percentage formulas and identify variables for Part b. Create and analyze an overall summary table for Part c to compare with Part a.

Step by step solution

01

Understanding the Problem

We're given data on death penalty decisions in Kentucky based on the race of the defendant and the victim. We need to calculate percentages of death penalties, identify variables in the analysis, and create a summarized table ignoring victim's race.
02

Analyzing Part a (i)

We need to calculate the percentage of white defendants who received the death penalty with a white victim. Then, calculate the percentage of black defendants with a white victim. Use the formula: \(\text{Percentage} = \frac{\text{Number of Death Penalties}}{\text{Total Number of Defendants}} \times 100\). Apply this to the data for each group.
03

Analyzing Part a (ii)

Repeat the process from Step 2, but this time focus on cases where the victim was black. Calculate and compare the percentage of white defendants vs. black defendants who received the death penalty when the victim is black.
04

Identifying Variables for Part b

In part a, the **response variable** is whether the death penalty was given (yes or no). The **explanatory variable** is the race of the defendant, and the **control variable** is the race of the victim.
05

Constructing Summary Table for Part c

Create a \(2 \times 2\) table that summarizes the data without considering the race of the victim. Add up all the cases of death penalty outcomes and total defendants, irrespective of the victim's race, for both white and black defendants.
06

Calculating Overall Percentages for Part c

Use the summary table to calculate the overall percentage of white and black defendants who received the death penalty, this time without accounting for the victim's race. Compare these overall percentages to those calculated in part a.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding the Response Variable
In any study or statistical analysis, the response variable is the main aspect of interest鈥攖he result you're evaluating.
In this analysis of death penalty decisions in Kentucky, the response variable represents whether the death penalty was given or not to the defendant.
This variable is typically categorical, indicating the specific outcome of interest in response to varying conditions. Response variables are crucial because they tell us the effects or results after considering other variables in the study.
In this context, it directly relates to how often the death penalty is applied, making it the center of the study's conclusions. To ensure clarity, when analyzing such studies, always keep the response variable in focus:
- It's the outcome being measured.
- Helps determine the impact of other factors like race on decisions.
- Conclusions drawn are based on analyzing changes or patterns in the response variable.
Identifying the Explanatory Variable
The explanatory variable, often considered the independent variable, helps to explain or predict changes in the response variable.
In the case of the death penalty exercise, the explanatory variable is the race of the defendant. The explanatory variable provides context and background for the changes you observe in the response variable.
It helps answer questions like why or how often a particular outcome occurs:
  • It provides insight into potential biases based on the defendant's race.
    It can highlight disparities in judicial outcomes.
Analyzing the explanatory variable allows researchers to:
  • Develop hypotheses about potential causations.
  • Understand underlying factors influencing outcomes like the death penalty decisions.
By considering different explanatory variables, researchers can better predict or elucidate different patterns evident in the response variable.
Role of the Control Variable
Control variables are used to maintain consistency and ensure that the analysis results are accurate and unbiased.
In this study regarding the death penalty, the control variable is the race of the victim. Control variables help in isolating the relationship between the explanatory and the response variables.
They ensure that the effects noticed are genuinely due to the explanatory variable and not some unconsidered factor. Here's why control variables are important in studies like this:
  • They limit the impact of confounding variables.
    They help isolate the true relationship between race and death penalty outcomes.
  • They improve the validity of findings.
    By controlling certain factors, researchers can attribute changes in the response variable mainly to the explanatory variable.
In engaging with such studies, it's crucial to recognize what factors are controlled to better understand the potential implications and biases involved.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Living poorly A survey of residents of several Western countries estimated the percentage in each country who reported going without food or without health care or without adequate clothing sometime in the past year. For example, the estimated percentage was \(33 \%\) in the United States (the highest in the survey) and \(9 \%\) in Japan. Are the samples from the United States and Japan independent samples or dependent samples? Why?

You would like to determine what students at your school would be willing to do to help address global warming and the development of alternatively fueled vehicles. To do this, you take a random sample of 100 students. One question you ask them is, "How high of a tax would you be willing to add to gasoline (per gallon) in order to encourage drivers to drive less or to drive more fuel-efficient cars?" You also ask, "Do you believe (yes or no) that global warming is a serious issue that requires immediate action such as the development of alternatively fueled vehicles?" In your statistical analysis, use inferential methods to compare the mean response on gasoline taxes (the first question) for those who answer yes and for those who answer no to the second question. For this analysis, a. Identify the response variable and the explanatory variable. b. Are the two groups being compared independent samples or dependent samples? Why? c. Identify a confidence interval you could form to compare the groups, specifying the parameters used in the comparison.

A clinical psychologist wants to choose between two therapies for treating severe cases of mental depression. She selects six patients who are similar in their depressive symptoms and in their overall quality of health. She randomly selects three of the patients to receive Therapy \(1,\) and the other three receive Therapy 2 . She selects small samples for ethical reasonsif her experiment indicates that one therapy is superior, she will use that therapy on all her other depression patients. After one month of treatment, the improvement in each patient is measured by the change in a score for measuring severity of mental depression. The higher the score, the better. The improvement scores are Therapy 1: 30,45,45 Therapy 2: 10,20,30 Analyze these data (you can use software, if you wish), assuming equal population standard deviations. a. Show that \(\bar{x}_{1}=40, \bar{x}_{2}=20, s=9.35,\) se \(=7.64\), \(d f=4,\) and a \(95 \%\) confidence interval comparing the means is (-1.2,41.2) b. Explain how to interpret what the confidence interval tells you about the therapies. Why do you think that it is so wide? c. When the sample sizes are very small, it may be worth sacrificing some confidence to achieve more precision. Show that a \(90 \%\) confidence interval is \((3.7,36.3) .\) At this confidence level, can you conclude that Therapy 1 is better?

The National Health Interview Survey conducted of 27,603 adults by the U.S. National Center for Health Statistics in 2009 indicated that \(20.6 \%\) of adults were current smokers. A similar study conducted in 1991 of 42,000 adults indicated that \(25.6 \%\) were current smokers. a. Find and interpret a point estimate of the difference between the proportion of current smokers in 1991 and the proportion of current smokers in 2009 . b. A \(99 \%\) confidence interval for the true difference is \((0.042,0.058) .\) Interpret. c. What assumptions must you make for the interval in part b to be valid?

A graduate teaching assistant for Introduction to Statistics (STA 2023) at the University of Florida collected data from students in one of her classes in spring 2007 to investigate whether study time per week (average number of hours) differed between students in the class who planned to go to graduate school and those who did not. The data were as follows: Graduate school: \(\quad 15,7,15,10,5,5,2,3,12,16,15,37,\) 8,14,10,18,3,25,15,5,5 No graduate school: 6,8,15,6,5,14,10,10,12,5 Using software or a calculator, a. Find the sample mean and standard deviation for each group. Interpret. b. Find the standard error for the difference between the sample means. Interpret. c. Find a \(95 \%\) confidence interval comparing the population means. Interpret.
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.