The strategy of the courtroom is a subtle thing. Common sense would say that a criminal who admits guilt is treated more leniently while a defiant criminal gets a harsher sentence. To see if this is...

The strategy of the courtroom is a subtle thing. Common sense would say that a criminal who admits guilt is treated more leniently while a defiant criminal gets a harsher sentence. To see if this is actually true, data was gathered from criminal courts to determine if criminals who plead guilty receive lighter sentences than those who plead guilty. Below is a small portion of that data set:

Sentence Served Plea

24 8.75 Not Guilty

33.5 6.5 Not Guilty

25.5 6.5 Guilty

18 12.5 Not Guilty

18.5 11 Guilty

44.5 14.5 Not Guilty

38.5 20 Not Guilty

50.5 22 Not Guilty

12.5 1 Guilty

102 10.75 Guilty

30 1.5 Guilty

The Variables are:

a) Sentence: Sentence Length (in months).

b) Served: Actual sentence served (in months).

c) Plea: either a not guilty plea or a guilty plea.

For this you should:

i) Perform a two sample
t-test (using
a
= 0.05) to compare the sentences given, and the sentences served, by those who plead guilty and those who do not. (So you’ll need to perform two separate two-sample
t-tests).

ii)
State and address all of the assumptions required for the
t-tests.

iii) Answer the question “Do criminals who plead guilty get more lenient treatment than those that plead not guilty?”