Empirical examinations of power-control theory find that girls who grow up in egalitarian families are more likely to be delinquent than girls who grow up in paternalistic families.

Yes, this is true, and can be seen in the power control theory made by John Hagan. In this theory, patriarchal families are one with the father having full control over the family. In egalitarian families, the rules are reversible and the tendency would be that the mother would exert less control on their daughters than their sons. This would be a factor in the delinquency rate of girls that grow up in egalitarian families.

The answer is true. As stated by Hagan, "As mothers gain power comparative to husbands, daughters gain liberty relative to sons." Over the egalitarian family structure, daughters are understood as more equal and can go in the workforce. Since not as much of control is applied on the daughter in the egalitarian family, they are given more possibility to take part in delinquent behavior, just as the sons are in patriarchal families. But, boys are still more probable to get involve in dangerous behavior. And the opposite of this goes to the patriarchal structure.