Question

If you had infinite time and resources, how would you go about creating a sampling distribution for samples of size n = 5 from a given population?

Answer 1

The distribution of population parameter can be obtained from the sample. To estimate

population parameter which can be done by collecting the data from the population. However

the sample introduces some sampling error which is unknown because we do not know the

population distribution. And if we have enough time and resources, this sampling error can be

minimize by taking multiple sample from the population. For example we want to estimate the

population parameter and variance thus we take the multiple sample of size, n (given n= 5)

and calculate the mean variance for each sample. Since the each sample may have different

shape and distribution, the large number of samples would form a new distribution, called a

sampling distribution. This distribution of the sample parameter close to the population

parameter. The figure below shows the multiple sample distribution as the population

distribution.

Now taking example with multiple sample data (size, n = 5) obtained from a population as shown below,

The histogram for the sample data is shown below,

And the mean and standard deviation estimate obtained for the sample mean is,

Mean	124.6143
Standard deviation	6.646959