Many people believe that criminals who guilty tend to get lighter sentences than

Question

Many people believe that criminals who guilty tend to get lighter sentences than those who are convicted in trials The accompanying table summarizes randomly selected sample data for defendants in burglary cases. All of the subjects had price prison sentences. Use a 0.05 significance level to test 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? Determine the null and alternative hypotheses. A 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. B. H_0: The sentence (sent 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. C. H_0: Pleading guilty reduces a defendant's chance of going to prison. H_1: Pleading guilty does not reduce a defendant's change of going to prison. D. 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. Determine the test statistic. x^2 =

Explanation / Answer

X2 = 8.085

Observed O guilty plea Not guilty plea Total sent to prison 389 65 454 not sent 543 52 595 Total 932 117 1049 Expected E=rowtotal*column total/grand total guilty plea Not guilty plea Total sent to prison 403.363 50.637 454 not sent 528.637 66.363 595 Total 932 117 1049 chi square =(O-E)^2/E guilty plea Not guilty plea Total sent to prison 0.511 4.0741 4.586 not sent 0.390 3.109 3.499 Total 0.902 7.183 8.0845

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