Student researchers wanted to see whether a person€™s reaction time is affected by the time of day. They had a computer program that would display a red circle. When it changed to yellow, the subjects were to click the mouse as fast as they could and the computer would calculate the reaction time. The researchers had their subjects perform this test at 10:00 am and again at 10:00 pm, recording the reaction time for each student at each time. They randomly determined which time of day was done first for each of their subjects. Here are their hypotheses.
Null: There is no association between time of day and reaction times (μ_d= 0).
Alternative: There is an association between time of day and reaction times (μ_d‰  0).
The students found the following results for reaction times in seconds:

a. What is the explanatory variable in this study? Is it categorical or quantitative?
b. What is the response variable in this study? Is it categorical or quantitative?
c. What is the observed statistic in this study?
d. Assuming a true null hypothesis, we simulated this study and found 1,000 mean differences that are shown in the null distribution below. Based on where the observed statistic lies in this distribution, does the p-value appear to be fairly small?

e. What is the standardized statistic for this test?
f. Based on your standardized statistic from part (e), is there strong evidence that reaction times differ between morning and night? Explain.

Transcribed Image Text:

Morning Night Difference Mean 0.244 0.306 -0.062 Standard deviation 0.052 0.084 0.082 Mean = 0.000 SD = 0.023 -0.06 -0.04 -0.02 0.02 0.04 0,06 Average difference