A study was carried out to assess the effect of alcohol on pilots. Ten pilots performed a series of routine tasks at a simulated altitude of 25, 000 feet. Each pilot performed the tasks in a completely sober condition and then three days later the pilot repeated the tasks after drinking alcohol. The response variable is the time (in seconds) of appropriate performance of the tasks. Bigger times are better. The null hypothesis is that alcohol has no effect, and the alternative is that performance degrades after alcohol use. The data are provided below along with summaries. pilot no alcohol alcohol difference
1 261 185 76
2 565 375 190
3 900 310 590
4 630 240 390
5 280 215 65
6 365 420 -55
7 400 405 -5
8 735 205 530
9 430 255 175
10 900 900 0

In order to assess the effect of alcohol on pilots, we are interested in the time difference between the no alcohol and alcohol conditions that the pilot was performing the tasks. Which statistic is most appropriate to address this problem?

a. X¯d∼N(μ=195.6,σ=72.8905)
b. X1¯−X2¯∼N(μ=195.6,σ=100.7493)
c. X1¯−X2¯∼tdf=19(μ=195.6,σ=100.7493)