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 47 cables and apply weights to each of them until they break. The 47 cables have a mean breaking weight of 777.4 lb. The standard deviation of the breaking weight for the sample is 15.5 lb.

Find the 90% confidence interval to estimate the mean breaking weight for this type cable.

( , )

Your answer should be rounded to 2 decimal places.

Answer 1

Given that,

= 777.4

s =15.5

n = 47

Degrees of freedom = df = n - 1 =47 - 1 = 46

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

t /2,df = t0.05,46 = 1.679 ( using student t table)

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

= 1.679 * ( 15.5/ 47) = 3.72

The 90% confidence interval estimate of the population mean is,

- E < < + E

777.4 - 3.72 < <777.4+ 3.72

773.68< < 781.12

( 773.68,781.12)