Question

1. 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.

2. A colleague of yours is struggling to make a decision on sample size. What advice would you provide to your colleague in terms of larger or smaller sample sizes? Why?

Please answer both questions correctly and completely.

Answer 1

Null hypothesis:- Whites in suburban areas who are convicted of more than 3 offences receive same prison sentences as the whites who are convicted of 3 or less offences.

Alternative Hypothesis:-Whites in the suburban areas who are convicted of more than 3 offences receive longer prison sentences than the whites who are convicted of 3 or less offences.

Here we can test for the mean.

If the sample size is small and population standard deviation is unknown then we use t test ..otherwise Z test.

Since the standard error of sample mean is inversely proportional to sample size... hence in order to reduce the unknown variability thw sample size should be large enough so that cost of the experiment can be maintained.