Report a Chi-Square test of Independence and use a 5% significance level. Choose the correct P-value picture. [ Select ] ["F", "D", "E", "
Report a Chi-Square test of Independence and use a 5% significance level. Choose the correct P-value picture. [ Select ] ["F", "D", "E", "
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Report a Chi-Square test of Independence and use a 5% significance level.
Choose the correct P-value picture. [ Select ] ["F", "D", "E", "A", "C", "B"]

Transcribed Image Text:The image consists of six panels (A to F) displaying different statistical distributions and their corresponding p-value areas, often used to interpret hypothesis test results. Each panel includes a curve representing a probability distribution and a shaded region indicating the p-value area.
**Panel A:**
- A right-skewed distribution curve with shading in the right tail.
- Labeled as "22.27, df=4" indicating chi-square distribution with 4 degrees of freedom.
**Panel B:**
- A symmetrical distribution around zero with two tails shaded.
- Labeled as "22.27, df=4", showing a two-tailed test for the same distribution.
**Panel C:**
- Right-skewed distribution similar to Panel A but with different shading.
- Marked as "22.27, df=9" representing a chi-square distribution with 9 degrees of freedom.
**Panel D:**
- Symmetric distribution with two tails shaded.
- Defined by "-22.27, 0, 22.27, df=9", illustrating a two-tailed test.
**Panel E:**
- Symmetrical distribution with two tails shaded.
- Labeled "0, 22.27, df=3", indicating a two-tailed test for a distribution with 3 degrees of freedom.
**Panel F:**
- A right-skewed distribution with shading in the right tail.
- Denoted as "22.27, df=3", showcasing a one-tailed test for a distribution with 3 degrees of freedom.
These panels represent different scenarios typically used in hypothesis testing, showing the critical values and p-value areas based on the test statistic and degrees of freedom.

Transcribed Image Text:**Recidivism Analysis Based on Treatment Received**
**Introduction**
Use the information below to answer the *recidivism* questions that follow.
The data and segmented bar chart below are "data on recidivism, as measured by re-arrest of persons who have committed at least one previous offense." We are looking to see if recidivism rate is influenced by the type of treatment received. *(Recidivism means a return to criminal behavior.)*
*Data from "Statistics for Experimenters" by Box Hunter Hunter.*
**Data Table**
The table displays the observed counts of individuals based on their recidivism rate and treatment received. The treatments considered are No Psychotherapy, Individual Therapy, and Group Therapy.
| **Observed Counts** | **Treatment Received** | | | | **Total** |
|-----------------------------|-----------------|-----------------|-------------|---------|--------|
| | No Psychotherapy | Individual Therapy | Group Therapy | | |
| **Recidivism Rate** | | | | | |
| Never back in prison | 12 | 9 | 20 | 41 |
| Back in prison within one year | 24 | 41 | 10 | 75 |
| Back in prison in 1-10 years | 25 | 32 | 13 | 70 |
| **Total** | 61 | 82 | 43 | **186** |
**Analysis**
This table helps in understanding the relationship between types of psychological treatment received and subsequent recidivism rates among individuals. It breaks down the results according to:
- **Never back in prison**: Showing how many remain crime-free.
- **Back in prison within one year**: Indicating early relapse into criminal behavior.
- **Back in prison in 1-10 years**: Showing delayed recidivism.
The totals provide insight into overall trends and effectiveness of different treatments.
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