Final answer:
The correct answer is option (d) the time participants were given to complete the problems.
Step-by-step explanation:
In the context of an experiment in psychology, researchers aim to investigate the relationship between variables. The independent variable is the factor that is manipulated or controlled by the experimenter to examine its impact on another variable.
In the scenario given, where a researcher is determining whether working under time pressure causes people to make more errors on moderately difficult math problems, the independent variable is (d) the time participants were given to complete the problems. This is because the experimenter has control over the amount of time allocated to the participants and is intentionally varying this to measure its effect.
The goal of the study is to observe the impact of this manipulation on the number of errors, which would be the dependent variable. This is because the dependent variable is what the researcher measures to see the effect of the independent variable. To ensure validity, the experiment would need to control for other potential lurking variables that may influence the outcome. Proper experimental design involves random assignment of participants to different conditions and control of other variables to isolate the effect of the independent variable.