An electroencephalogram (EEG) is often used to measure brain, or neural, activity. Research suggests that transcendental...

An electroencephalogram (EEG) is often used to measure brain, or neural, activity. Research suggests that transcendental meditation – TM – produces a simplified state of rest and relaxation resulting in an EEG with smaller than normal 22 variance. Suppose normal brain activity has a variance of σ^2 =15volts. A random sample of patients who can achieve the state of consciousness associated with TM will be selected and their brain activity will be measured during meditation. The resulting information will be used to test the research hypothesis.

State the null and alternative hypotheses in terms of variance.
DescribeType1and Type2 errors in this context.If there is evidence to suggest that TM decreases the variance in brain activity, the National Science Foundation will commit more money for TM research.

i. Which error is more serious for the National Science Foundation? Why?

ii. Which errors more serious for TM researchers? Why?

Solutions

Expert Solution

Null Hypothesis H0: The variance in brain activity by transcendental meditation (TM) is 15 volts. That is,

Alternative Hypothesis Ha: The variance in brain activity by transcendental meditation (TM) is less than15 volts. That is, .

Type 1 error is rejection of a true null hypothesis. In this context, Type 1 error is that we conclude the variance in brain activity by transcendental meditation (TM) is less than15 volts but in reality the variance in brain activity by transcendental meditation (TM) is normal and equal to 15 volts.

Type 2 error is failure to reject a false null hypothesis. In this context, Type 2 error is that we cannot conclude the variance in brain activity by transcendental meditation (TM) is less than15 volts and the variance is normal but in reality the variance in brain activity by transcendental meditation (TM) is less than15 volts.

If there is evidence to suggest that TM decreases the variance in brain activity, the National Science Foundation will commit more money for TM research. Thus, if we conclude the variance in brain activity by transcendental meditation (TM) is less than15 volts, National Science Foundation will commit more money for TM research but the money will be lost if in reality the variance in brain activity by transcendental meditation (TM) is normal and equal to 15 volts. So, type 1 error is more serious for the National Science Foundation.

ii.

If TM researchers cannot conclude that the variance in brain activity by transcendental meditation (TM) is less than15 volts but in reality the variance in brain activity by transcendental meditation (TM) is less than15 volts, TM researchers would fail to prove their success of the research. So, type 2 error is more serious for TM researchers.

orchestra answered 1 year ago

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