At the Statistics Canada Web site, you can find the percent of adults in each province or territory who have at least a university certificate, diploma, or degree at bachelor's level or above. It makes no sense to find x bar for these data and use it to get a confidence interval for the mean percent μ in all 13 provinces or territories. Why not?

To understand why it is not appropriate to find an x-bar (sample mean) and use it to calculate a confidence interval for the mean percent (μ) in all 13 provinces or territories, let's break down the scenario:

The dataset you mentioned provides information on the percent of adults in each province or territory who have at least a university certificate, diploma, or degree at the bachelor's level or above. In this case, the percentage of adults having these qualifications is a proportion (not a continuous variable like height or weight) specific to each province or territory.

A confidence interval estimates the range within which we are confident that the true population mean lies. However, in this case, we are not interested in estimating the mean percent for all provinces or territories; rather, we want to determine the proportion within each specific province or territory separately.

To calculate a confidence interval for a proportion, we typically use binomial or normal approximations based on the number of successes (in this case, adults with the stated educational qualifications) and the sample size. This method allows us to estimate the true proportion within each province or territory, not the mean percentage across all of them.

Therefore, since the goal is to obtain separate estimates for each province or territory and not a single mean percentage for all of them, it is not appropriate to calculate an x-bar and utilize it to construct a confidence interval for the mean percent (μ) across all 13 provinces or territories.