A manufacturer of hard safety hats for construction workers is concerned about the mean and the variation of the forces

[answerhappygod]

A manufacturer of hard safety hats for construction workers is
concerned about the mean and the variation of the forces its
helmets transmits to wearers when subjected to an external force.
The manufacturer has designed the helmets so that the mean force
transmitted by the helmets to the workers is 800 pounds (or less)
with a standard deviation to be less than 40 pounds. Tests were run
on a random sample of n = 40 helmets, and the sample mean and
sample standard deviation were found to be 800 pounds and 47.5
pounds, respectively. Do the data provide sufficient evidence, at
the α=0.05 level, to conclude that the population standard
deviation exceeds 40 pounds?