Question:
a) An article "Does it pay to plead guilty? Differential Sentencing and the Functioning of Criminal Courts" [Law and Society Review, 1981] considered the punishments metered out to 255 individuals found guilty of robbery. All individuals had previous convictions. Of the 191 who pleaded "guilty", 101 were given custodial sentences, whilst of the 64 who pleaded "not guilty" 56 were sent to prison.
Present this information in the form of a 2 by 2 contingency table. Carry out a test to determine if the proportion of individuals sent to prison differs significantly for those pleading "guilty" and those pleading "not-guilty"?
b) A promotions panel in a metropolitan police force considered applications from 15 officers who applied for senior positions during one year. The table below records the outcome, classified by gender of the applicant:
|
Gender
|
Promoted
|
Not promoted
|
Total
|
|
Male
|
7
|
1
|
8
|
|
Female
|
2
|
5
|
7
|
|
Total
|
9
|
6
|
15
|
Assuming that these fifteen applications can be considered a random sample of all applications made within the police force calculate the exact probability of this arrangement occurring by chance assuming that males and females are equally likely to be promoted. Test the hypothesis that males are significantly more likely to be promoted.