You ask a group of 8 adults to participate in a reaction time task after completing exercise. The history of research indicates that performance on many tasks actually improves with physical activity. You record the following comprehension times (in seconds) required to identify the two meanings of ambiguous sentences, such as, “The children ran in the house” or “The sailors liked the port.” You hypothesize that a small amount of physical exercise will decrease the participants’ comprehension times (that is, you predict faster/smaller time scores with a small amount of physical activity). The mean comprehension time on this task for persons who have not completed any physical activity recently is = 2.1 seconds. The scores below are the comprehension times for 8 persons in your sample who completed exercise for 30 minutes prior to engaging in the task.
X
(comprehension time, in seconds)
1.1
0.6
1.2
0.6
1.3
1.0
0.8
1.1
With α = .01, determine the critical value of z* or t* that needs to be employed here. The value of the appropriate of z* or t* is: