## Simple Random Sampling

Simple random sampling, also called chance selection, refers to a method of collecting a sample in which each and every element in the population is given an equal chance of being included in the sample. In other words, all the elements in the population have equal probabilities of being chosen. The method assumes that if the population is sufficiently large and the sample is chosen purely on a random basis, the sample is likely to represent all the groups in the population.

Example 1: Simple Random Sampling

Suppose we wish to come up with a sample of 50 CFA level 1 candidates given that there are 5000 level 1 candidates in total:

One approach may involve numbering each of the 5000 candidates, placing them in a basket and shaking the basket. Next, we would randomly draw 50 numbers from the basket, one after the other without replacement.

A more scientific approach may also involve the use of random numbers where all the 5000 candidates are numbered in sequence (from 1 to 5000). We may then use a computer to randomly generate 50 numbers between 1 and 5000, where a given number represents a particular candidate who can be identified by their name/admission number.

The underlying feature in random sampling is that each element in the population must have equal chances of being chosen.

## Sampling Distribution

Sampling distribution refers to the distribution of possible outcomes of a sample statistic such as the mean that would be derived from equal-sized samples drawn from the same population. It’s a probability distribution of a sample statistic from multiple samples.

Example 2: Sampling Distribution

Suppose we wish to estimate the mean return on 1000 different stocks in a country; we could select a sample of 50 stocks and analyze their financial results to calculate the sample mean return. Suppose we repeatedly selected equally-sized samples from the population; we would end up with several different estimates of the unknown population mean return. The distribution of these sample means would effectively give us the sampling distribution of the mean.

One condition stands; the different samples should be equally sized and drawn from the same population. This would ensure that the results are reliable and relevant.

Define simple random sampling and a sampling distribution.

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