Question

Can a six-month exercise program increase the total body bone mineral content (TBBMC) of young women?
That is, we are interested in determining if the exercise program is beneficial, i.e., the mean percent change is positive.

Assume a sample of 25 subjects is taken.

A team of researchers is planning a study to examine this question.
Based on the results, they are willing to assume that σ = 2 for the percent change in TBBMC over the six- month period.
They also believe that a change in TBBMC of 1% is important, so they would like to have a reasonable chance of detecting a change this large or larger.

Calculate the power of this test.

Answer 1

Can a six-month exercise program increase the total body bone mineral content (TBBMC) of young women?
That is, we are interested in determining if the exercise program is beneficial, i.e., the mean percent change is positive. Assume a sample of 25 subjects is taken. A team of researchers is planning a study to examine this question. Based on the results, they are willing to assume that σ = 2 for the percent change in TBBMC over the six- month period. They also believe that a change in TBBMC of 1% is important, so they would like to have a reasonable chance of detecting a change this large or larger.

Calculate the power of this test.

Let α =0.05

MINITAB used:

Power and Sample Size

1-Sample Z Test

Testing mean = null (versus > null)

Calculating power for mean = null + difference

α = 0.05 Assumed standard deviation = 2

Results

Difference	Sample Size	Power
1	25	0.803765

power of this test = 0.8038