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 50 cables and apply weights to each of them until they break. The 50 cables have a mean breaking weight of 778.9 lb. The standard deviation of the breaking weight for the sample is 15.6 lb.

Find the 95% confidence interval to estimate the mean breaking weight for this type cable.

( , )

Your answer should be to 2 decimal places.

Answer 1

وم solution: - Sample standard deviation is given so need to t confidence interve with following formula XzE X = Sample mean, E = tx s t = tu S- Sample standard de viation h = Sample size X z 778.9 sz 15.6 nz 50 n-1 Find t value using t table for Inputtrar dif = degree of freedom 50-| -49 two tail and ant. confidence level. tvalu=2.01 ad exact value of dif not prevent an Table then use ifr approximate vales.

: E = 2.01 2 15.6 х 09 9.91 X 10.6 = 60 E=2101 X 15.6 7,071 E = 2.01 X 2.2061 Ez4, 434261 lower limit = F-E = 778.9 -4.4342 = 774.46 upper limit EXTE = 778,9 + 4.4342 = 783.33