Chapter 5.12, Problem 26E

The administrator of a nursing home would like to do a time-and-motion study of staff time spent per day performing nonemergency tasks. Prior to the introduction of some efficiency measures, the average number of person-hours per day spent on these tasks was μ = 16. The administrator wants to test whether the efficiency measures have reduced the value of μ. How many days must be sampled to test the proposed hypothesis if she wants a test having α = .05 and the probability of a Type II error of at most .10 when the actual value of μ is 12 hours or less (at least a 25% decrease from the number of hours spent before the efficiency measures were implemented)? Assume σ = 7.64.