Question

3. Safety Helmets 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 825 pounds and 48.5 pounds, respectively. Do the data provide sufficient evidence, at the α = 0.05 level, to conclude that the population standard deviation exceeds 40 pounds? Hint: We are testing for population variance (single sample). Here, large variance means there is a safety issue. So when we look from the workers’ safety perspective, we would like to see if the variance of force that is transmitted to the workers’ head exceed 402 =1600 pounds. Therefore, the null hypothesis states H0: s2=402 =1600, where the alternative hypothesis states H1: s2 >1600, indicating a right tailed test.

Answer 1