Final answer:
Two samples from the same stable and in-control process may have different sample means due to random sampling error, but on average, they should be close to the population mean, especially with sufficiently large sample sizes.
Step-by-step explanation:
When two samples are taken from the same stable and in-control process and are of the same size, it is still possible for the sample means to differ. This is because each sample will likely contain different individual values even though they are from the same population. According to the Central Limit Theorem for Sample Means, if the sample size is sufficiently large, the distribution of the sample means will be approximately normal, and the mean of the sample means will equal the population mean. However, in practice, individual sample means can vary due to random sampling error.
It's important to note that when dealing with two samples from the same stable and in-control process, we expect that on average the sample means will be close to each other and to the population mean, especially as sample size increases. However, due to random variation, the means of individual samples may not be exactly the same.
In summary, while we expect sample means to be similar for a stable and in-control process, each sample is an independent snapshot of the population, and thus, some variation between sample means is to be expected.