An operating system for a personal computer has been studied extensively, and it is known that the standard deviation of the response time following a particular command is σ = 8 milliseconds. A new version of the operating system is installed, and we wish to estimate the mean response time for the new system to ensure that a 95% confidence interval for μ has length at most 5 milliseconds.
(a) If we can assume that response time is normally distributed and that σ = 8 for the new system, what sample size would you recommend?
(b) Suppose that we are told by the vendor that the standard deviation of the response time of the new system is smaller, say σ = 6; give the sample size that you recommend and comment on the effect the smaller standard deviation has on this calculation.