Question

A sample of ultimate tensile strength observations (ksi) was taken. Use the accompanying descriptive statistics output from Minitab to calculate a 99% lower confidence bound for true average ultimate tensile strength, and interpret the result. (Round your answer to two decimal places.)

Answer 1

Answer:

The 99% lower confidence bound for the true average ultimate tensile strength is $\mu\geq134.53$.

With these lower confidence bound we can claim that there is a 99% chance that the real ultimate tensile strength is greater than 134.53.

Step-by-step explanation:

The question is incomplete. The desctiptive statistics are the ones attached.

We have to calculate a 99% lower confidence bound for true average ultimate tensile strength.

For a 99% lower confidence bound, the z-value is z=2.33.

The margin of error is

$E=z\sigma/\sqrt{n}=2.33*4.59/\sqrt{153}=10.69/12.37=0.86$

Then, the 99% lower confidence bound for the true average ultimate tensile strength is:

$\mu\geq M-z\sigma/\sqrt{n}\\\\\mu\geq 135.39-0.86\\\\\mu\geq 134.53$

The experiment is probably done to estimate with a certain degree of confidence the minimum tensile strength of a population of elements, by evaluating a sample.

With these lower confidence bound we can claim that there is a 99% chance that the real ultimate tensile strength is greater than 134.53.