Question

he Cambridge Study of delinquent development was undertaken in N. London to investigate the links between criminal behavior in young men and socioeconomic factors of the upbringing. A cohort of 395 boys was followed for about 20 years starting at the age of 8 or 9. All boys attended 6 schools located near the research office.

The table below provides the following summary statistics relating family income and convictions.

Income level

	Inadequate	adequate	Comfortable or higher
No convictions	47	128	90
Convicted	43	57	30

• Can we consider the cohort of these boys to be a random sample of a certain portion of the male youth of UK?
• What is the necessary assumption that needs to be made about the income group assignment of these boys for the duration of the study?
• Identify the random variables of the data set. What is the type of these variables?
• Construct the appropriate plot of these data.
• Do the two random variables seem to have an association? Which one can be used as explanatory?   

Answer 1

1. No, as the cohort of these boys is considered from 6 schools near the research office, this cohort can not be a representative of the male youth of the UK.

2. The necessary assumptions are i) The sample should be randomly collected, ii) Normality of the data set, iii) Homoskedisticity of the data set, iii) multicollinearity of the data set.

3. There are two random variables: Convictions and Income level. The type of these variables is factor or treatment.

5. Yes the random variables seem to have association. ANOVA can be used as explanatory.