Researchers are studying the impact of alcohol consumption on a person’s ability to perform a simple task. Five subjects complete a small puzzle while sober, and then again after drinking three glasses of wine. The times (in seconds) are shown below, as well as some summary statistics:
Subject 1 2 3 4 5 mean std. dev.
Sober (S) 109 132 248 155 202 169.2 55.9
After Wine 141 128 290174 260 198.6 72.5
(AW)
Assume that all appropriate normality conditions are satisfied. We would like to conduct a hypothesis test to determine whether there is evidence that the true mean time to complete a puzzle is longer after consuming three glasses of wine.