Back in Chapter 9, the Central Limit Theorem showed us that samples are typically representative of the populations from which their drawn. It follows then that the mean of a randomly selected sample should provide a fair estimate of the corresponding population mean.
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Using the sample mean to estimate the population mean may seem obvious, but a good estimator for a population parameter must have certain characteristics to be dependable. In this video I discuss the qualities of a good estimator: unbiasedness, consistency, and relative efficiency.
Estimation questions are pretty easy to solve. If you can follow along the solution to the confidence interval estimation question in this video, then you’re just about prepared for the worst this chapter has to offer!
Here’s another typical estimation question, but now we’re also asked to interpret our results. Getting this interpretation right is can be tricky – The wording has to be just right to avoid making a common mistake (which they WILL be looking for on the exam).
Smaller confidence intervals are better as they give us a more precise estimate of the mean. A simple way to affect the width of the interval is to change the confidence level. See how.
We shouldn’t have to give up confidence in order to have a smaller (more precise) interval estimate. In this video I cover all of the other factors that we can change to affect the width of the confidence interval, and I discuss why increasing the sample size is by far the best approach.
If larger samples give us better estimates, then how large does a sample need to be (as a minimum) in order to ensure we keep our estimation errors small?
Test your understanding of Chapter 10: Introduction to Estimation – each question is accompanied by a mini-video lecture showing you how I decided which solution was the correct one.