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 40 cables and apply weights to each of them until they break. The 40 cables have a mean breaking weight of 775.3 lb. The standard deviation of the breaking weight for the sample is 14.9 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

Solution :

Given that,

= 775.3

s = 14.9

n = 40

Degrees of freedom = df = n - 1 = 40 - 1 = 39

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

t _/2,df = t_0.05,39 = 1.685

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

= 1.685 * (14.9 / 40)

= 3.97

The 95% confidence interval estimate of the population mean is,

- E < < + E

775.3 - 3.97 < < 775.3 + 3.97

771.33 < < 779.27

(771.33 , 779.27)