In given problem, suppose that the population standard deviation is 1.0 and that the true average reduction in consumption for the entire population in the area is µD = 0.1. For a sample size of 60 and α = 0.01, what is the power of the test?

Problem
A study is undertaken to determine how consumers react to energy conservation efforts. A random group of 60 families is chosen. Their consumption of electricity is monitored in a period before and a period after the families are offered certain discounts to reduce their energy consumption. Both periods are the same length.

The difference in electric consumption between the period before and the period after the offer is recorded for each family. Then the average difference in consumption and the standard deviation of the difference are computed.

The results are D‾ = 0.2 kilowatt and S_D = 1.0 kilowatt. At α = 0.01, is there evidence to conclude that conservation efforts reduce consumption?