Final answer:
The proportional limit stress for a population cannot be determined from a sample mean and standard deviation without additional statistical analysis or information. Therefore, the correct answer is that it cannot be determined.
Step-by-step explanation:
The proportional limit stress for a sample of specimens, based on a given sample mean and standard deviation, cannot be exactly known for the entire population of joint specimens without additional statistical analysis.
Based on the data provided (sample mean proportional limit stress of 8.49 MPa and a sample standard deviation of 0.78 MPa for 12 specimens), the proportional limit stress represents the mean value of stress that the specimens in your sample can withstand before they start to deform non-linearly. However, this is only representative of the sample itself, not necessarily the entire population.
To determine the proportional limit stress for the population, we would need confidence intervals or perform hypothesis testing, which would require more information, such as the population distribution characteristics and the desired confidence level. Thus, the correct answer based on the options provided is 3) Cannot be determined.