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 43 cables and apply weights to each of them until they break. The 43 cables have a mean breaking weight of 774.3 lb. The standard deviation of the breaking weight for the sample is 15.4 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,

= 774.3

s =15.4

n = 43

Degrees of freedom = df = n - 1 = 43- 1 = 42

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

t /2,df = t0.05,42 = 1.682    ( using student t table)

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

= 1.682 * ( 15.4/ 43) = 3.95

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

- E < < + E

774.3- 3.95 < < 774.3+ 3.95

770.35 < <778.25

( 770.35 ,778.25 )