In a study analyzed by the Laboratory for Interdisciplinary Statistical Analysis at

Virginia Tech, a group of subjects was asked to complete a certain task on the

computer. The response measured was the time to completion. The purpose of the

experiment was to test a set of facilitation tools developed by the Department of

Computer Science at the university. There were $10$ subjects involved. With a random

assignment, five were given a standard procedure using Fortran language for

completion of the task. The other five were asked to do the task with the use of the

facilitation tools. The data on the completion times for the task are given here

a$)$ Assuming that the population distributions are normal, and variances are

the same for the two groups, support or refute the conjecture that the

facilitation tools increase the speed with which the task can be

accomplished.

b$)$ a$)$ Assuming that the population distributions are normal, but variances

are NOT the same for the two groups, support or refute the conjecture that

the facilitation tools increase the speed with which the task can be

accomplished.