The key thing in statistical inference is, based on sample information draw conclusion about the population from where the sample was drawn.
There are two types of statistical inference methods. We can estimate population parameters and we test hypothesis about these parameters.
There are two ways to estimate the value of a population parameter.
The first one is so called point estimate. It is a single number that is the best guess for the population parameters. And the second one is the interval estimate. It is a range of values within which we expect the parameters to fall around.
- The statistic calculated from the sample is a point estimate of the corresponding population parameter.
– The sample average is a point estimate of the true population mean.
– The sample proportion is a point estimate of the population proportion.
- The SE of the statistic provides a measure of the precision of the estimate
– A larger SE indicates a less precise point estimate
– A smaller SE indicates a more precise point estimate
Let’s take an example. Imagine we would like to estimate one things.
(1) What is the average height of south Indian man?
We’re going to consider the south India as population and collected a simple random sample of 20,000 people from this population.
We want to estimate the population mean based on the sample. The most intuitive way to do this is to simply take the sample mean. That is, to estimate the average height of all south Indian people, take the average height for the sample. Let’s think all 20,000 samples that we collected the sample mean ¯x = 172.72 cm. Then the height 172.72 cm is called a point estimate of the population mean. If we can only choose one value to estimate the population mean, this is our best guess.
Suppose we take a new sample of another 30,000 people and recompute the mean; we will probably not get the exact same answer that we got first time. Point estimates generally vary from one sample to another and this sampling variation suggests our estimate may be close, but it may not be exactly equal to the parameter. So, the moral of the story is point estimates are not exact and we should not expect our estimate to be very good.