In Exercise 11.39, we tested to determine whether the installation of safety equipment was effective in reducing person-hours lost to industrial accidents. The null and alternative hypotheses were

H0: μ = 0

H1: μ < 0

With σ = 6, α = .10, n = 50, and μ = the mean percentage change. The test failed to indicate that the new safety equipment is effective. The manager is concerned that the test was not sensitive enough to detect small but important changes. In particular, he worries that if the true reduction in time lost to accidents is actually 2% (i.e., μ = −2), then the firm may miss the opportunity to install very effective equipment. Find the probability that the test with σ = 6, α = .10, and n = 50 will fail to conclude that such equipment is effective. Discuss ways to decrease this probability.