Report a Chi-Square test of Independence and use a 5% significance level. Choose the correct P-value picture.                             [ Select ]                          ["F", "D", "E", "

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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"]           

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: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.
**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.
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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