Final answer:
The correct research hypothesis is b. Hi : X1 ≠ X2, indicating the researcher believes there is a difference in reaction times between decaffeinated and caffeinated coffee drinkers without specifying a direction of the difference.
Step-by-step explanation:
The correct research hypothesis for the scenario where a researcher wants to know if there is a difference in reaction time for participants who drink decaffeinated coffee as compared with those who drink caffeinated coffee is b. Hi : X1 ≠ X2. This is known as the alternative hypothesis and suggests that there is a difference in reaction time between the two groups. The notation X1 and X2 represent the mean reaction times for the decaffeinated and caffeinated coffee groups, respectively. The hypothesis signifies that the researcher expects there to be a difference but does not specify the direction of the difference.
Studies like this are part of establishing cause-and-effect relationships through scientific experiments. Through careful design, such as random assignment and possibly a double-blind procedure, researchers can decrease biases and increase the reliability of their findings. The consumption of caffeine and its effects on human reaction time is an area of interest in such research. By stating the alternative hypothesis as X1 ≠ X2, the researcher keeps the possibility open that either decaffeinated or caffeinated coffee could lead to faster or slower reaction times without the need for a directional hypothesis at this stage.