Question

3.         Provide the null hypothesis and the statistical test that would be used for the following research hypothesis: Whites in suburban areas who are convicted of more than 3 offenses receive longer prison sentences than whites in suburban areas that are convicted of 3 offenses or less.

Answer 1

The test is to check whether the whites in suburban areas,who have been convicted of more than 3 crimes , receives longer prison sentences than whites in suburban areas , who have been convicted of three or less crimes.

We can carry out in the following manner.

We select a sample of whites in suburban area( of size n1)who have been convicted of more than 3 crimes ,and a sample of whites in suburban area ( of size n2) who have been convicted of 3 or less crimes.

We then denote m1 as the mean prison length of the first category population and m2 as the mean prison length of the second category population.

Our aim is to test the Null Hypothesis that

H₀: m1>m2.