Final answer:
The mean of c31 "row mean" could be different from the population mean due to outliers or data skewness. With a large sample size, the sample mean is expected to be more accurate due to the law of large numbers. The confidence intervals constructed from the sample are likely to contain the population mean at a high percentage, typically around 90-95%, reflective of their confidence level.
Step-by-step explanation:
The mean of c31 "row mean" can differ from the mean of the original population depending on data distribution and sample size. In a scenario where the sample size is large, according to the law of large numbers, we would expect the sample mean to be closer to the population mean, which in this context is mentioned to be 100. However, if the data is right-skewed or contains significant outliers, as noted in the provided data, those outliers can cause the sample mean to diverge from the actual population mean by increasing it, in the case of positive outliers, or decreasing it, if negative outliers are present.
When referencing the construction of confidence intervals and their capacity to contain the true population mean, if we assume that we generate 100 confidence intervals, about 90 to 95 percent of them are expected to contain the actual population mean if they have been calculated at 90 to 95 percent confidence levels respectively. Therefore, as more samples are taken and confidence intervals created, a consistent proportion of them is expected to contain the population mean. This is reflective of the probability inherent in confidence interval construction.
If confidence intervals for a certain sample do not contain the true population mean, this could suggest that either the sample is not representative of the population or that extreme values are influencing the sample mean, thereby affecting the accuracy of the confidence intervals derived from that sample.