A manufacturer of hard safety hats for construction workers is concerned regarding the mean and the variation of the forces its helmets transmit to wearers when subjected to a standard external force. The manufacturer desires the mean force transmitted by helmets to be 800 lb., well under the legal 1000-lb. limit, and desires σ to be less than 40. Tests were run on a random sample of n = 40 helmets, and the sample mean and variance were found to be equal to 825 lb. and 2350 lb.2, respectively.
a. If μ = 800 and σ = 40, is it likely that any helmet subjected to the standard external force will transmit a force to a wearer in excess of 1000 lb.? Explain.
b. Do the data provide sufficient evidence to indicate that when subjected to the standard external force, the helmets transmit a mean force exceeding 800 lb.?
c. Do the data provide sufficient evidence to indicate that σ exceeds 40?