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 774.6 lb. The standard deviation of the breaking weight for the sample is 15.1 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

Solution :

Given that,

= 774.6

s = 15.1

n = 50

Degrees of freedom = df = n - 1 = 50 - 1 = 49

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t _/2,df = t_0.005,49 = 2.680

Margin of error = E = t_/2,df * (s /n)

= 2.680 * (15.1 / 50)

= 5.72

The 99% confidence interval estimate of the population mean is,

- E < < + E

774.6 - 5.72 < < 774.6 + 5.72

768.88 < < 780.32

(768.88 , 780.32)