A professor is interested in the relationship between the number of hours students study for
a quiz and their quiz grades. She asked each student to record the number of hours that
he/she studied for the final exam. She also recorded the students’ grades in percentages
(ex. 86%). What technique should the professor use to analyze the data?
a. t-test for two independent samples
b. t-test for matched pairs
c. Chi square test for independence
d. correlation
To analyze the relationship between the number of hours students study for a quiz and their quiz grades, the professor should use the correlation technique. This technique measures the strength and direction of the relationship between two variables. In this case, the variables are the number of hours studied and the quiz grades.
To conduct a correlation analysis, the professor needs to follow these steps:
1. Calculate the correlation coefficient: The professor can use a statistical software or calculator to calculate the correlation coefficient, also known as Pearson's correlation coefficient (r). This coefficient ranges from -1 to +1, with a value of -1 indicating a perfect negative correlation, +1 indicating a perfect positive correlation, and 0 indicating no correlation.
2. Interpret the correlation coefficient: Once the professor obtains the correlation coefficient, she can interpret the strength and direction of the relationship. If the coefficient is close to -1 or +1, it suggests a strong relationship. If it is close to 0, it suggests a weak or no relationship. The sign (+/-) of the coefficient indicates the direction of the relationship (positive or negative).
3. Assess the significance: To determine if the correlation coefficient is statistically significant, the professor needs to calculate the p-value associated with the correlation coefficient. A p-value less than a predetermined significance level (commonly 0.05) indicates a statistically significant relationship.
Therefore, in this scenario, the professor should choose option d. correlation as the technique to analyze the data. This will help her understand the strength and direction of the relationship between the number of hours studied and the quiz grades.