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.

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

Answer:

Given that,

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.

Income level,

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

(1).

For checking randomness of given data:

Total number of boys =395

Total number of categories=6

If homegenety occurs in each categories there will be 395/6 boys. this is expected frequency.

For checking randomness of data, we use chat square distribution Xn^2:n=5 given by,

< : Test fail randomness of data set.

According to above result. Now we can't consider cohart of these boys to be a random.

(2).

These is no connection between the income level and criminal behaviour in boys.

(3).

Attribute/quality/characteristics data or Dichotomy data or Dichotomy classification.

	Inadequate	adequate	Comfortable or higher	Total
No convictions	47(60.38)(i)	128(124.11)	90(80.54)(ii)	265
Convicted	43(29.62)	57(60.88)	30(39.45)(iii)	130
Total	90	185	120	395

Note:

(i). (90)(265)/(395)=60.38

(ii). (120)(265)/(395)=80.54

(iii). (120)(130)/(395)=39.45

The above table is known as contegency tabel observed frequency are given and expected are given and expected frequency are calculated and written is braket '()' in the table above.

The test statistics for hypotheses given is ('2)

with degree of frequency

(r-1)(c-1)

=(2-1)(3-1)

=1(2)

=2

Note:

We are checking independency is (1) we are checking randomness,

=2.964+0.121+3.3010+6.044+0.2+2.263

=14.9429

=5.991

< we reject the test hypotheses.

Yes there is association between both income level and criminal behaviour.

Watching numerical measure we can say strongly that indw income level is higher convicted.

Inadequate-conv=6.049

Adequate-conv=0.29

Higher - conv =2.263