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 is

significantly less than40.

1.Calculate the test statistic for this problem. Round your answer to two decimal places.

2.Determine the p-value for alower one-sided alternative hypothesis (left-tail test).The alternative hypothesis for this problem is H1:2< 1600 lbs2

3.What is the rejection region at the 10% level of significance for the test on the variance for a left-tailed alternative hypothesis?The alternative hypothesis for this problem is H1:2< 1600 lbs2.