Question

A group of engineers developed a new design for a steel cable. They need to estimate the amount of weight the cable can hold. The weight limit will be reported on cable packaging. The engineers take a random sample of 40 cables and apply weights to each of them until they break. The 40 cables have a mean breaking weight of 775-3 lb. The standard deviation of the breaking weight for the sample is 14.9 lb.

Answer 1

Solution Given data x=775.3 14.9 40 To find the 90% confidence interval to breaking weight for this type cable Here 2=1-confidence interval estimate the mean L=1- 90 loo L = 1-0.9 L = 0.1 degrees of freedom df = 40-1 df = 39 critical value = +212, df =t, 0.1 2139 t 0.05, 39 1.685 t critical Value

90% confidence Interval for M = Xit 2/2df (un = 775.3+ 1.685 X 114.9 140 =775.3+ (1.685 x 2.3559 =775.3 + 3.9699 = [ 11 775.3–3.9697, 775.373.9691] = [771.33, 779.27] Therefore the 90% confidence interval to estimate the mean breaking weight weight for this type cable is [771.33, 779. 1779.21)