A manufacturer of hard safety hats for construction workers is concerned regarding the mean and variation of forces its helmets transmit to wearers when subjected to the standard external force. The manufacturer desires the mean force transmitted by helmets to be 800 lb., well under legal 1000-lb. limit, and desires σ to be less than 40. Tests were run on the 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 standard external force will transmit force to a wearer in excess of 1000 lb.? Discuss.
b. Do the data provide sufficient evidence to point out 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 point out that σ exceeds 40?