# Testing of Hypothesis

A manufacturer of hard hats for construction workers is concerned about 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 pounds (or less), well under the legal 1000-pound limit, and desired  to be less then 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 pounds and 2350 pounds2, respectively.

a. If  = 800 and  = 40, how likely is it that any helmet subjected to the standard external force will transmit a force to the wearer in excess of 1000 pounds?

b. Test the hypothesis that, when subjected to the standard external force, the helmets transmit a mean force exceeding 800 pounds, and determine the p-value.

c. Test the hypothesis that  exceeds 40.

https://brainmass.com/statistics/hypothesis-testing/testing-of-hypothesis-192938

#### Solution Summary

The solution contains a testing of hypothesis problem and the determination of P-value.