The Cambridge Study of delinquent development was undertaken in N. London to inv
ID: 3291313 • Letter: T
Question
The 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. Does the data suggest that young adults who grow in households with inadequate income levels have higher conviction rates than their peers who come from households with adequate or higher incomes? Use Confidence interval estimation to derive your conclusions. Can we assert that young adults who grow in households with inadequate incomes will have higher propensity for criminal convictions than their peers who come from households with better incomes? Does low household income push young men to crime? The term young adults should be interpreted as young aExplanation / Answer
Assume samples are independent.
From given information, n inadequate-convicted=43, n inadequate total=90 (47+43),
n adequate/higher-convcted=87 (57+30), n adequate/higher total=305 (128+90+57+30).
Therefore, phat inadequate-convicted=n inadequate-convicted/n inadequate total=43/90=0.4777
phat adequate/higher-convicted=87/305=0.2852
The 95% c.i for (p inadequate-convicted-p adequate/higher-convicted)=(phat inadequate-convicted-phat adequate/higher-convicted)+-zalpha/2 sqrt[phat inadequate-convicted(1-phat inadequate-convicted)/n inadequate-convicted total+phat adequate/higher-convicted(1-phat adequate/higher-convicted)/n adequate/higher-convicted total)
=(0.4777-0.2852)+-1.96 sqrt[0.4777(1-0.4777)/90+0.2852(1-0.2852)/305]
=(0.0776, 0.3075)
The 95% confidence interval does not contain 0, therefore, the data sugegsts that young adults who grow in households with inadequate income levels have higher conviction rates than their peers who come from households with adequate or higher incomes.
This can not be asserted until an experiment is conducted where the effect of other variables (confounding ones) which affect propensity for criminal convictions are minimized or eliminated.