Final answer:
The correct interpretation of a correlational study showing a positive relationship between the number of hours mothers worked and incidences of child delinquency is that it suggests the need for further research to establish causation, as correlation does not imply causation. Other factors could be at play, and experimental research would be required to control for these variables.
Step-by-step explanation:
If a correlational study of a large sample of children found a positive relationship between the number of times children got into trouble with the law and the number of hours their mothers worked outside the home, this result would not indicate a causal relationship. Instead, it would suggest a need for further experimental research to establish causation. Correlation does not imply causation; other factors such as after-school childcare availability, community support, or socioeconomic status might also play significant roles in child behavior and could potentially confound the relationship observed.
While increased hours spent by mothers working correlates with higher instances of juvenile delinquency, we cannot conclude that one causes the other without controlling for these other variables. For instance, if policing patterns change due to wartime efforts or societal stressors, this could lead to more juveniles being labeled as delinquents for behaviors previously disregarded. Additionally, the presence of more maternal or parental supervision is shown to be beneficial to child well-being, emphasizing the importance of considering the broader context when interpreting such studies.
Therefore, option b) is the correct interpretation of the given result from a correlational study: It suggests a need for further experimental research to establish causation rather than directly proving or indicating it.