Final answer:
In a correlational study, you can only conclude that there is a correlation between the variables, not a cause-and-effect relationship. Alternative explanations, such as the influence of third variables, must be considered, and experimental evidence would be required to establish causality.
Step-by-step explanation:
When you read that a correlational study has found that children who participate in more extracurricular activities have higher self-esteem, you could only conclude that there is a correlation between these two variables. It is important to remember that correlation does not establish cause-and-effect relationships. Therefore, the correct conclusion from such a study is d) a third variable may be influencing both extracurricular activities and self-esteem.
For instance, the correlational study discussed does not definitively tell us whether participating in extracurricular activities causes higher self-esteem (a), or if children with higher self-esteem are more likely to participate in more extracurricular activities (b). Moreover, claiming a cause-and-effect relationship (c) without further experimental evidence would be misleading and incorrect.
The role of third variables, such as family income, parental support, or even personality traits, could potentially influence both a child's engagement in extracurricular activities and their level of self-esteem. Therefore, while these relationships are important for forming hypotheses, experiments with controlled variables are necessary to determine causality.