Final Answer:
Sure, an example of a quantitative research question aimed at investigating the relationship among variables could be: "What is the correlation between hours of study (X) and exam scores (Y) among college students?"
Step-by-step explanation:
In this research question, the primary aim is to discern the relationship between two variables: hours of study (X) and exam scores (Y). To investigate this relationship quantitatively, correlation analysis is an apt statistical method. Correlation coefficient (r) is used to measure the strength and direction of the linear relationship between these variables. It ranges from -1 to 1, where 1 indicates a perfect positive correlation, -1 implies a perfect negative correlation, and 0 suggests no correlation.
The calculation of the correlation coefficient involves the summation of products of the differences between each variable value and its mean, divided by the product of their standard deviations. For instance, if there are paired observations (X₁, Y₁), (X₂, Y₂), ... (Xₙ, Yₙ), the formula for the correlation coefficient (r) is:
\[r = \frac{n(\sum X_iY_i) - (\sum X_i)(\sum Y_i)}{\sqrt{[n\sum(X_i^2) - (\sum X_i)^2][n\sum(Y_i^2) - (\sum Y_i)^2]}}\]
By employing this formula and plugging in the values for hours of study and corresponding exam scores from the collected data, one can compute the correlation coefficient to ascertain the strength and direction of the relationship between these variables.
Conclusively, the stated research question is designed for a quantitative study to explore the connection between study hours and exam scores. Utilizing correlation analysis allows for the quantification of this relationship, offering insights into whether more study hours correlate positively, negatively, or neutrally with exam performance among college students.