Medicine and Clinical Studies
An electroencephalogram (EEG) is often used to measure brain, or neural, activity expressed as electrical voltage. Research suggests that transcendental meditation (TM) produces a simplified state of rest and relaxation resulting in an EEG with smaller than normal variance. Suppose normal brain activity has variance s2 5 15 volts2 . A random sample of patients who can achieve TM will be selected, and their brain activity will be measured during TM. The resulting information will be used to test the research theory.
a. State the null and alternative hypotheses in terms of σ2.
b. Describe a type I and a type II error in this context.
c. If there is evidence to suggest TM decreases the variance in brain activity, then the National Science Foundation (NSF) will commit more money for TM research. Which error is more serious for the NSF? Why? Which error is more serious for TM researchers? Why?