Question

Cable Strength As a reminder, here again is the example from the previous page. 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 45 cables and apply weights to each of them until they break. The mean breaking weight for the 45 cables is xbar =768.2 lb. The standard deviation of the breaking weight for the sample of cables is s = 15.1 lb. In the example we concluded the following. We are 95% confident that the mean breaking weight for all cables of this type is between 763.7 lb and 772.7 lb. In other words the 95% confidence interval is (763.7, 772.7).

Suppose the engineers want to make a 99% confidence interval. They plan to use the same sample of 45 cables. Use the applet to find the critical T-value they will use in the computation of the margin of error.

Construct the 99% confidence interval. Enter the lower bound of the interval (the smaller number). If necessary, round to two decimal places.

What is the upper bound of the 99% confidence interval? If necessary, round to two decimal places.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 768.2

sample standard deviation = s = 15.1

sample size = n = 45

Degrees of freedom = df = n - 1 = 45-1 = 44

t _/2,df = 2.69

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

=2.69 * (15.1 / 45)

Margin of error = E = 6.06

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

- E < < + E

768.2 - 6.06 < < 768.2 + 6.06

762.14 < < 774.26

(762.14,774.26)

lower bound =762.14

upper bound = 774.26