An experimental surgical procedure is being studied as an alternative to the old method. Both methods are considered safe.

An experimental surgical procedure is being studied as an alternative to the old method. Both methods are considered safe. Five surgeons perform the operation using both methods on two patients matched by age, sex, and other relevant factors, with the time to complete the surgery (in minutes) recorded below. 

At the 1% level of significance, does the new method decrease the average length of the surgical procedure? Give the conditions under which this test is valid.