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 46 cables and apply weights to each of them until they break. The 46 cables have a mean breaking weight of 779 lb. The standard deviation of the breaking weight for the sample is 15.4 lb. Find the 99% confidence interval to estimate the mean breaking weight for this type cable. Your answer should be to 2 decimal places.

Answer 1

Formula for Confidence Interval for Population mean when population Standard deviation is not known

Given
Sample Mean : : Sample mean breaking weight	779
Sample Standard Deviation : s: Sample standard deviation of the breaking weight	15.4
Sample Size : n : Number of randomly selected cables	46
Degrees of freedom : n-1	45
Confidence Level :	99
=(100-99)/100 = 0.01	0.01
/2=0.01/2=0.005	0.005
	2.6896

99% confidence interval to estimate the mean breaking weight for this type cable:

99% confidence interval to estimate the mean breaking weight for this type cable: = (772.89,785.11)