In: Math

# The strategy of the courtroom is a subtle thing. Common sense would say that a criminal...

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.

Variables:

a) sentence: Sentence Length (in months).
b) served: Actual sentence served (in months).
c) plea: either a not guilty plea or a guilty plea.

Sentence Served Plea
24 8.75 Not Guilty
33.5 6.5 Not Guilty
25.5 6.5 Gulity
18 12.5 Not Guilty
18.5 11 Gulity
44.5 14.5 Not Guilty
38.5 20 Not Guilty
50.5 22 Not Guilty
12.5 1 Gulity
102 10.75 Gulity
30 1.5 Gulity

Perform a two sample t-test to compare the sentences served by those who plead guilty and those who do not.

State and address all of the assumptions required for the t-test.

Use boxplots to illustrate your data, and describe how they relate to your results.

Do criminals who plead guilty get more lenient treatment than those that plead not guilty? As much as possible, relate your comments to specific results.

## Solutions

##### Expert Solution

Perform a two sample t-test to compare the sentences served by those who plead guilty and those who do not.

State and address all of the assumptions required for the t-test.

Assumption of T-test

-Dependent variables must be continuous.
-The data values must be indepedent of each other.
-They must be drawn from a normally distributed population
- There must be no outliers.

Use boxplots to illustrate your data, and describe how they relate to your results

Do criminals who plead guilty get more lenient treatment than those that plead not guilty? As much as possible, relate your comments to specific results.​​​​​​​

Yes, criminals who plead guilty get more lenient treatment than those that plead not guilty.

This is evident from the box plot wherein we see that the years served by guilty is much less than not guilty.

Also, the hypothesis shows that mean year served by those plead guilty is less than those who have not.

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