Federal workplace safety standards for noise levels state that personal protective equipment is required if the time-weighted sound level at a work site exceeds 90 dBA. Suppose that this is...

Federal workplace safety standards for noise levels state that personal protective equipment is required if the time-weighted sound level at a work site exceeds 90 dBA. Suppose that this is interpreted as saying that the mean sound level at a site should not significantly exceed 90 dBA. At one location on its fabrication floor, a manufacturer records sound levels over 10 randomly selected time intervals. Should the company begin requiring ear protection, if:

(a) x = 81:2; s = 10:4; α = 0:1?

(b) x = 97:2; s = 10:4; α = 0:1?

(c) Why would α = 0:1 be more reasonable than α = 0:01 in this situation?