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 not 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 α = 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?”