Question

. In an online experiment, participants were asked to react to a stimulus. Upon seeing a blue screen, participants were instructed to press a key and the reaction time was measured in seconds. The same participant is also asked to press a key when seeing a red screen, with the reaction time measured. (The first color tested was randomly selected for each participant.) The results of 6 randomly sampled participants are below. Is the reaction time to the blue stimulus different from the reaction time to the red stimulus at the 1% level of significance? (assume the population differences are approximately normally distributed)

participant 1 2 3 4 5 6

blue 0.582 0.481 0.841 0.267 0.685 0.450

red 0.408 0.407 0.542   0.402 0.456 0.533

Conduct a full hypothesis test. Be sure to:

• state the test and calculator test

• check conditions

1. state the hypotheses

2. find the differences between the pairs, sample mean, sample standard deviation, degrees of freedom and calculate the test statistic

3. state the level of significance

4. find the p-value and draw/shade the graph

5. make a decision

6. write a conclusion

Answer 1