Final answer:
To explore the relationship between height and GPA, a correlation or regression analysis would be the appropriate statistical methods. Correlation assesses the strength and direction of the relationship, while regression can also provide a predictive model.
Step-by-step explanation:
When researchers are interested in the relationship between two variables, such as height and academic achievement (represented by GPA), they often use statistical methods to analyze the data. In this case, a correlation would be appropriate to determine the strength and direction of the relationship between height and GPA. If they wish to predict GPA based on height, a regression analysis would provide the best method since it not only indicates whether there is a relationship but also describes the nature of the relationship through a predictive equation.
Since the question asks for a test to investigate the relationship between two continuous variables, options a, b, c, f, and g (which involve comparing means or testing hypotheses about means) are not suitable. Correlation (option e) and regression (option d) are the correct statistical tests to use in this scenario. They will allow researchers to explore the potential association between height and GPA, as well as to create a model for prediction if needed.