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 limits and the standard deviation to be less than 40. A random sample of 41 helmets was tested and the sample mean and variance were 825 pounds and 2350 pounds². Manufacturer wants to know if the data provides sufficient evidence to indicate the standard deviation exceeds 40. Find the test statistic (round to four decimal places), p-value for an upper one-sided alternative hypothesis (right -tail test)(alternative hypothesis is H₁:o²>1600lbs²), and what is the rejection region at 5% level of significance for the test on the variance for a right-tailed alternative hypothesis(alternative hypothesis is H₁:o²>1600lbs²), state your conclusion using a significance level of 0.05(alternative hypothesis is H₁:o²>1600lbs²),, and calculate a 95% confidence interval for the variance of force on the helmets(rounded to four decimal places).