In an experiment conducted online at the University of Mississippi, study participants are asked to react to a stimulus. In one experiment, the participant must press a key on seeing a blue screen. Reaction time (in seconds) to press the key is measured. The same person is then asked to press a key on seeing a red screen, again with reaction time measured. The results for six randomly sampled study participants are as follows:

(a) Why are these matched-pairs data?
(b) In this study, the color that the student was first asked to react to was randomly selected. Why is this a good idea in this experiment?
(c) Is the reaction time to the blue stimulus different from the reaction time to the red stimulus at the α = 0.01 level of significance?
(d) Construct a 99% confidence interval about the population mean difference. Interpret your results.
(e) Draw a boxplot of the differenced data. Does this visual evidence support the results obtained in part (b)?

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1 2 34 Participant 3 Blue Red 456 0.582 0.481 0.841 0.267 0.685 0.450 0.408 0.407 0.542 0.402 0.456 0.533