To compare the effect of stress in the form of noise on the ability to perform a simple task, 70 subjects were divided into two groups. The first group of 30 subjects acted as a control while the second group of 40 were the experimental group. Although each subject performed the task in the same control room, each of the experimental group subjects had to perform the task while loud rock music was played. The time to finish the task was recorded for each subject and the following summary was obtained:
Control n1 = 30, xbar1 = 15 minutes, s1 = 4 minutes
Experimental n2 = 40, xbar2 = 23 minutes, s2 = 10 minutes.
a) Find a 99% confidence interval for the difference in mean completion times for these two groups.
b) Is there a sufficient evidence to indicate a difference in the average time to completion for the two groups ? Explain.