Many people believe that criminals who plead guilty lend to get lighter sentence

Question

Many people believe that criminals who plead guilty lend to get lighter sentences then those who are convicted in trials. The accompanying table summarizes randomly selected sample data for defendants in burglary cases. All of 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 dependent, would these results suggest that you should encourage a guilty plea? Determine the null and alternative hypothesis. A. H_0: Pleading guilty reduces a defendant's chance of going to prison. H_1: Pleading guilty does not reduce a defendant's chance of going to prison. B. H_0: The sentence (sent to prison or not sent to prison) is not independent of the plea. H_1: The sentence (send to prison or not sent to prison) is independent of the plea. C. H_0: Pleading guilty does not reduce a defendant's chance of going to prison. H_1: Pleading guilty reduces a defendant's chance of going to prison. D. H_0: The sentence (sent to prison or not sent to prison) is independent of the plea. H_1: The sentence (sent to prison or not sent to prison) is not independent of the plea. Determine the test statistic. x^2 = (Round to three decimal places as needed) Determine the p-value of the statistic. p-value = (Round to four decimal places as needed.)

Explanation / Answer

X2 =1.078

p value =0.2991

Observed O guilty plea Not guilty plea Total sent 414 57 471 Not sent 568 64 632 Total 982 121 1103 Expected E=rowtotal*column total/grand total guilty plea Not guilty plea Total sent 419.331 51.669 471 Not sent 562.669 69.331 632 Total 982 121 1103 chi square =(O-E)^2/E guilty plea Not guilty plea Total sent 0.068 0.5500 0.618 Not sent 0.051 0.410 0.460 Total 0.118 0.960 1.078

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