4. A recent study compared substance use, delinquency psychological well-being, and so- cial support anong various family types. lor a sample of urban Aincan-American ado- lescent males (M. Zimmerman et al., Child Development. Vol 66. 1995. pp. 1598-1613). The sample contained 108 subjects from single-mother households and 44 from house- holds with both biological parents. Delinquency was measured with four dichotomous items asking the youths if they had ever (i) been in trouble with the police. (ii) been at- rested, (iii) appeared before a juvenile court. or (iv) been incarcerated in the last year: the delinquency score was the number of items to which a youth answered yes. This score had a mean of 19 and standard deviation of 1.5 for single-mother households and a incan of 1.4 and standard deviation of 1.5 for houscholds with both biological parents.

a) Construct a 99% confidence interval for the difference between the true means for the populations represented by this sample. Interpret

b) Test the hypothesis of equal means against the alternative of unequal means. Report the P-value and interpret.

c) Explain the conespondence between the results of

(a) and

(b)

d) Do you think that delinquency is nonnally distributed for each household type? Ex- plain. and indicate whether this has any effect on your inferential analyses.