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 u in all 13 provinces or territories. Why not?
You need to weight the provinces for province population first. Some of them are very sparsely populated.
To understand why it doesn't make sense to find x-bar (sample mean) and use it to get a confidence interval for the mean percent (u) in all 13 provinces or territories, we need to consider the nature of the data and the population in question.
First, let's define x-bar and u in this context. x-bar represents the sample mean, which is the average percent of adults with a university certificate, diploma, or degree at bachelor's level or above calculated from a sample of provinces or territories. On the other hand, u represents the population mean, which is the average percent of adults with the mentioned educational attainment in all 13 provinces or territories.
The problem arises because we are dealing with proportions or percentages in each province or territory, not continuous numerical data. In such cases, calculating the mean and applying confidence intervals for the population mean isn't appropriate. This is because the proportions are bounded between 0% and 100%, unlike continuous data that can span a range of values.
Instead, when dealing with proportions or percentages, it's more suitable to use confidence intervals around the proportion itself (p), which represents the true percentage in the population. This allows us to estimate the range within which the true proportion is likely to fall.
To calculate a confidence interval for the percent of adults with a university certificate, diploma, or degree at bachelor's level or above in all 13 provinces or territories, you would need to gather data from the entire population or use appropriate statistical methods for estimating proportions, such as using the sample proportions to construct a confidence interval. This differs from using x-bar and the usual methods for continuous data.
In summary, due to the nature of the data being proportions or percentages, it's more appropriate to use confidence intervals for the proportion (p) rather than the mean (u) when estimating the percentage in the entire population.