This topic introduces the basic concept of Sampling Distribution.
At the end of this lesson, you should be able to:
What is Statistical Sampling?
Sampling is the process of selecting units from a population of interest so that by studying the sample, we may generalize our results about the population from which the samples where chosen.
Very often, we make decisions based on a limited set of data. For example, thousands of boxes Quaker Life Cereals are produced every day. As a Production Manager, you need to ensure that mean weight of all the boxes of cereals (known as the population) is 360 gm.
It is very time consuming and costly to weigh all the boxes in production for that day. So, instead, we sample by weighing a limited number of boxes from the population. From the information obtained from these samples, we can reach an inference or conclusion about the mean weight of the cereal boxes in production.
Below diagram illustrates the concept.
Reasons for Sampling
In many cases, sampling is more feasible then studying the entire population. Click below to find out some reasons for sampling. Click on video to find out what are reasons.
Sampling Error
It is unlikely the mean of a sample will be exactly equal to the mean of the population. For example, in the Quaker Life Cereals example, it is unlikely that the sample mean of the 30 boxes is the same the as the population mean of 360 gm.
If the sample mean of the 30 boxes is 380 gm and the population mean in 360 gm, then the Sampling Error = (380 - 360 ) = 20 gm.
Hence, Sampling Error is defined as the difference between a sample mean, x ̅ and its corresponding population mean, μ.
Having Sampling Error is expected, as it is unlikely the mean of a sample will be exactly equal to the mean of the population. How then can we use the sample mean to estimate the population mean? This question is answered in the next topic on Sampling Distribution of the Sample Mean.
What are some of the reasons we do sampling? (Select those that apply)