A manufacturer of hard safety hats for construction workers

A manufacturer of hard safety hats for construction workers is concerned about the mean and the variation of the forces 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 1000-pound legal limit, and the standard deviation to be less than 40. A random sample of 31 helmets was tested and the sample mean and variance were found to be 825 pounds and 2350 pounds2, respectively. The manufacturer wants to know if the data provides sufficient evidence to indicate that the standard deviation exceeds 40.

Calculate a 99% confidence interval for the variance of force on the helmets. Round your answers to four decimal places.

Solution

Excel is used to calcute the confidence interval.

(n1)s2/2/2 2 (n1)s2/21/2

(1313.53,5113.62)