Question

A sample of 13 joint specimens of a particular type gave a sample mean proportional limit stress of 8.45 mpa and a sample standard deviation of 0.77 mpa. Calculate and interpret a 95% lower confidence bound for the true average proportional limit stress of all such joints.

Answer 1

The 95% lower confidence bound for the true average proportional limit stress of all joints is 7.993 MPa.

Step-by-step explanation:

To calculate the 95% lower confidence bound for the true average proportional limit stress of all such joints, we can use the formula:

Lower Confidence Bound = Sample Mean - (Critical Value * Sample Standard Deviation / sqrt(Number of Samples))

First, we need to find the critical value for a 95% confidence level. We can use the t-distribution table or an online calculator to find this value. Let's assume the critical value is 2.120.

Using the given values of Sample Mean = 8.45 MPa, Sample Standard Deviation = 0.77 MPa, and Number of Samples = 13, we can calculate the 95% lower confidence bound as follows:

Lower Confidence Bound = 8.45 - (2.120 * 0.77 / sqrt(13))

Lower Confidence Bound = 8.45 - (2.120 * 0.77 / 3.606)

Lower Confidence Bound = 8.45 - 0.457

Lower Confidence Bound = 7.993 MPa

Therefore, the 95% lower confidence bound for the true average proportional limit stress of all such joints is 7.993 MPa.