Many people that criminals who plead guilty tend to get higher sentences than th

Question

Many people that criminals who plead guilty tend to get higher sentences than those who are convicted in trials. The accompanying table summarizes randomly selected sample data for defendants in burglary cases All or the subjects had prior prison sentences. 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? H_1: Pleading guilty reduces a defendant's chance of going to prison. H_0: The sentence (sent to prison or not sent to prison) is not independent of the plea. H_1: The sentence (sent to prison or not sent to prison) is independent of the plea. H_0 : Pleading guilty reduces a defendants chance of going to prison. H_1: Pleading guilty does not reduce a defendant's chance of going to prison. Determine the test statistic. x^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 lest 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? 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. 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. There is not sufficient evidence to warrant rejection of the claim that the sentence is independent to the plea. The results do not encourage pleas for guilty defendants. 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.

Explanation / Answer

Null and alternative hypotheses:

Ho: The sentence is independent to the plea.

H1: The sentence is not independent to the plea.

The statistical software output for this problem is:

Contingency table results:
Rows: var1
Columns: None

Chi-Square test:

Hence,

X2 = 3.724

P - value = 0.0536

Option C is correct for conclusion part.

Guilty Plea Not Guilty Plea Total Sent to Prison 385 68 453 Not Sent to Prison 541 67 608 Total 926 135 1061

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