Prof. C is studying a population of the elementary school pupils in a school district with data on all its children. Another prof. suggests he calculate a confidence interval to estimate the mean age of the children. Prof C responds that it is not necessary. Explain why Prof. C is correct.
You included every single child so your results are exact.
Prof. C is correct in this case because he has access to data on all the children in the school district. In statistics, a confidence interval is typically used when we only have a sample of the population and want to estimate a parameter, such as the population mean. By calculating a confidence interval, we can provide a range of values within which we are reasonably confident that the parameter lies.
However, in Prof. C's situation, he already has data on all the children in the school district. This means he has the complete population and not just a sample. When working with the entire population, there is no need to estimate the parameter using a confidence interval because the true mean age is known.
So, Prof. C can directly calculate the mean age of the children without needing to rely on statistical estimation techniques like confidence intervals.