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hance of going to prison. f going to prison. f going to prison. More Info Sent to Prison Not Sent to Prison Guilty Plea 353 535 Not Guilty Plea 58 60

hance of going to prison. f going to prison. f going to prison. More Info Sent to Prison Not Sent to Prison Guilty Plea 353 535 Not Guilty Plea 58 60

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 10CYU
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11.10

## Evaluating the Effect of Guilty Pleas on Sentencing Outcomes Many people believe that criminals who plead guilty tend to receive lighter sentences than those who are convicted in trials. The accompanying table summarizes a study with randomly selected samples of defendants in burglary cases. All of the subjects had prior prison sentences. The study uses a 0.05 significance level to test whether the sentence (being sent to prison or not) is independent of the plea entered. If you were an attorney defending a guilty defendant, would these results suggest that you should encourage a guilty plea? ### Table Summary Below is the table summarizing the outcomes based on the plea type: | | Guilty Plea | Not Guilty Plea | |-------------------------|-------------|-----------------| | **Sent to Prison** | 353 | 58 | | **Not Sent to Prison** | 535 | 60 | ### Determine the Null and Alternative Hypotheses **Option C** has been marked as selected, indicating the appropriate hypotheses to be tested: - **Null Hypothesis (H₀):** The sentence (sent to prison or not sent to prison) is independent of the plea. - **Alternative Hypothesis (H₁):** The sentence (sent to prison or not sent to prison) is not independent of the plea. ### Instructions To evaluate whether encouraging a guilty plea is advantageous, consider these hypotheses alongside the statistical tests performed at the significance level of 0.05. This analysis will help determine if there is a significant association between plea type and sentencing outcome.
Transcribed Image Text:## Evaluating the Effect of Guilty Pleas on Sentencing Outcomes Many people believe that criminals who plead guilty tend to receive lighter sentences than those who are convicted in trials. The accompanying table summarizes a study with randomly selected samples of defendants in burglary cases. All of the subjects had prior prison sentences. The study uses a 0.05 significance level to test whether the sentence (being sent to prison or not) is independent of the plea entered. If you were an attorney defending a guilty defendant, would these results suggest that you should encourage a guilty plea? ### Table Summary Below is the table summarizing the outcomes based on the plea type: | | Guilty Plea | Not Guilty Plea | |-------------------------|-------------|-----------------| | **Sent to Prison** | 353 | 58 | | **Not Sent to Prison** | 535 | 60 | ### Determine the Null and Alternative Hypotheses **Option C** has been marked as selected, indicating the appropriate hypotheses to be tested: - **Null Hypothesis (H₀):** The sentence (sent to prison or not sent to prison) is independent of the plea. - **Alternative Hypothesis (H₁):** The sentence (sent to prison or not sent to prison) is not independent of the plea. ### Instructions To evaluate whether encouraging a guilty plea is advantageous, consider these hypotheses alongside the statistical tests performed at the significance level of 0.05. This analysis will help determine if there is a significant association between plea type and sentencing outcome.
Determine the test statistic. \( \chi^2 = \, \) (Round to three decimal places as needed.) Determine the P-value of the test statistic. P-value = \, (Round to four decimal places as needed.) Use a 0.05 significance level to test the claim that the sentence (sent to prison or not sent to prison) is independent of the plea. If you were an attorney defending a guilty defendant, would these results suggest that you should encourage a guilty plea? - A. There is sufficient evidence to warrant rejection of the claim that the sentence is independent of the plea. The results encourage pleas for guilty defendants. - B. There is not sufficient evidence to warrant rejection of the claim that the sentence is independent of the plea. The results do not encourage pleas for guilty defendants. - C. There is sufficient evidence to warrant rejection of the claim that the sentence is independent of the plea. The results do not encourage pleas for guilty defendants. - D. There is not sufficient evidence to warrant rejection of the claim that the sentence is independent of the plea. The results encourage pleas for guilty defendants.
Transcribed Image Text:Determine the test statistic. \( \chi^2 = \, \) (Round to three decimal places as needed.) Determine the P-value of the test statistic. P-value = \, (Round to four decimal places as needed.) Use a 0.05 significance level to test the claim that the sentence (sent to prison or not sent to prison) is independent of the plea. If you were an attorney defending a guilty defendant, would these results suggest that you should encourage a guilty plea? - A. There is sufficient evidence to warrant rejection of the claim that the sentence is independent of the plea. The results encourage pleas for guilty defendants. - B. There is not sufficient evidence to warrant rejection of the claim that the sentence is independent of the plea. The results do not encourage pleas for guilty defendants. - C. There is sufficient evidence to warrant rejection of the claim that the sentence is independent of the plea. The results do not encourage pleas for guilty defendants. - D. There is not sufficient evidence to warrant rejection of the claim that the sentence is independent of the plea. The results encourage pleas for guilty defendants.
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