Final answer:
Taking two separate samples from the same population would not likely produce identical means due to random variation. Sample means are expected to vary around the true population mean, with the concept of sampling distributions highlighting this variability. The likelihood of differing means increases with independent group means and unknown population variances.
Step-by-step explanation:
If you took two separate samples from the same population, they would not likely produce identical means. This is because each sample is subject to random variation, and even though the samples come from the same population, the randomness inherent in sampling means that each sample will probably have a slightly different mean. This can be explained by looking at the concept of sampling distributions, which predicts that the means of separate samples will vary around the true population mean, creating a distribution of sample means called the sampling distribution of the mean.
According to the Central Limit Theorem, the more samples we take, the closer the sample means will cluster around the population mean. However, unless the population is very small, no two samples will likely have means that are exactly identical. Variations between sample means are expected and are accounted for in statistical analysis.
Moreover, when hypothesis testing is performed on matched or paired samples, the situation discussed in the question differs; paired samples involve two measurements that are related and, thus, compared directly to each other. This is not the case with independent samples from the same population, which would more likely involve hypothesis tests concerning two independent group means where population variances may be unknown (as is commonly the case).