A state legislature mandates the each school district in its state must conduct an audit of the performance of the district’s students on the state reading exam. The purpose is to determine if there are any extreme increases in the individual schools in the district. There are currently four software programs that are capable of conducting the audits with varying degrees of efficiency. The state board of education hires an analyst to design a study to evaluate each of the software programs. The study will involve a random sample of schools running the software on their records. One of the metrics in the evaluation will be the amount of time that the software takes to complete the audit. From the application of the software in other states, the standard deviation in the time to complete the audit was 122.5 minutes. Determine how many schools are required in the study for each software program in order to be able to detect a difference in any pair of software programs of 5 hours using a level .05 test with a power of 90%.