Final answer:
Based on the given F-ratio df=3, 12 in a repeated-measures ANOVA, there were 4 subjects who participated in the research study.
Step-by-step explanation:
The question asks how many subjects participated in a repeated-measures research study based on an F-ratio with degrees of freedom (df) equal to 3, 12 from an ANOVA test. In a repeated-measures ANOVA, the numerator df (df between groups) is equal to the number of conditions minus one (k - 1), and the denominator df (df within subjects) equals the number of observations minus the number of conditions (n - k).
In this case, we have a numerator df of 3, which means there are 3 + 1 = 4 conditions. The denominator df is 12, which indicates the total number of observations minus the number of conditions (n - 4) equals 12. Solving for n gives us n = 12 + 4 = 16 observations. However, since this is a repeated-measures design, each subject is measured under each condition, implying that the total number of observations is the number of subjects times the number of conditions. Thus, the number of subjects would be 16 (total observations) divided by 4 (number of conditions), which gives us a total of 4 subjects.