SOLUTION: Many people believe that criminals who plead guilty tend to get lighter sentences than those who are convicted in trials. The accompanying table summarizes randomly selected sample

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Question 1083119: Many people believe that criminals who plead 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 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?
_ Guilty_Plea Not_Guilty_Plea
Sent_to_Prison 373 48
Not_Sent_to_Prison 568 33
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
Sent_to_Prison------ 373 48===421
Not_Sent_to_Prison---- 568 33===601
==================941==81==1022
The expected values are for the upper left: 421*941/1022, and the second row left 601*941/1022
Expected are
387.63==33.37
553.37==47.63
sum of (O-E)^2/E=0.55+4.46+0.38+6.49=11.88 (11.85 using TI-83)
The critical value is 3.84 at the 0.05 level
This is highly significant statistically; whether one should encourage it depends upon other factors, but this would be an important one. About 89% go to prison who plea and about 95% who don't.