Final answer:
The estimated population mean proportional limit stress is 8.47 MPa, and the margin of error for this estimate is 0.385 MPa.
Step-by-step explanation:
In this question, we are given a sample of 18 joint specimens, with a sample mean proportional limit stress of 8.47 MPa and a sample standard deviation of 0.77 MPa. We are asked to find the estimated population mean proportional limit stress and the margin of error for this estimate.
To estimate the population mean, we can use the formula: estimated population mean = sample mean.
In this case, the estimated population mean is 8.47 MPa.
The margin of error is calculated by multiplying the standard deviation by the critical value for a given level of confidence, divided by the square root of the sample size.
In this case, we need to determine the critical value for a given level of confidence. Let's assume a 95% level of confidence. The critical value for a 95% confidence level is approximately 1.96.
Now, we can calculate the margin of error using the formula: margin of error = (critical value * sample standard deviation) / square root of sample size.
Substituting the values into the formula, we get
margin of error = (1.96 * 0.77) / sqrt(18)
= 0.385 MPa.
Therefore, the margin of error for the estimate is 0.385 MPa.