This topic introduces the basic concept of Sampling Distribution.
At the end of this lesson, you should be able to:
Introduction
We learn that each time we do sampling to estimate population parameters, there is a high possibility of sampling error.
So, how can the Production Manager ensure that mean weight of the samples taken is indeed an accurate estimate of the mean weight of the population?
He can do so by taking say, 30 boxes of Corn Flakes and calculate its mean. By repeating this procedure many times, he will be able to calculate many sample means.
By organizing these sample means into a probability distribution, the result is called the sampling distribution of the sample mean.
As we will see in the next section, the mean of this sampling distribution is exactly equal to the population mean!
Sampling Distribution of the sample mean is the probability distribution of all possible sample means of a given sample.
Properties of a Sampling Distribution of the Sample Mean
Watch the video below to understand that the mean of the sample distribution and its standard deviation (also known as standard error of the mean) is related to the population parameters.
We have seen from previous section, when the population distribution of X is normal with mean μ and standard deviation σ, then the sampling distribution of the sample mean is also normally distributed.
You have learnt in the topic on Normal Probability Distribution that we can convert any normal variable to a standard normal variable using the formula:
In Sampling Distribution, the following formula will be used: