MAT 118 - Elementary Statistics 1. Student researchers wanted to know if a person's reaction time is affected by the time of day. They had their volunteers watch a screen and press a button when a circle changed from green to red. The researchers tested the subjects at 10:00AM and again at 10:00PM recording the reaction time for each student. The researchers used a random mechanism to determine what time of day each volunteer was their first attempt. The hypotheses and results for reaction times are below: Null: There is no association between time of day and reaction times (Ha = 0). Alternative: There is an association between time of day and reaction times (ud # 0). Morning Night Difference Mean 0.244 0.306 -0.062 Standard deviation| 0.052 0.082 0.084 a) A simulated null distribution is produced below. Mark on the graph the area(s) that represent the p-value. (Be mindful of the alternative hypothesis) Mean = 0.000 SD = 0.023 -0.06 -0.04 -0.02 0 0.02 0.04 0,06 Average difference b) Which of the following is most likely the p-value for this test? (1) 0.001 (ii) 0.10 (iii) 0.999 (iv) -2.70 c) Based on the information provided, calculate the standardized statistic. d) Approximate the 95% confidence interval for the mean difference in reaction times (morning - night) using the data provided above