What is simple random sampling?

Simple random sampling is a method of selecting a sample from a population where each member has an equal chance of being chosen.

In simple random sampling, each member of the population has an equal chance of being selected for the sample. This is achieved by assigning a unique number to each member of the population and using a random number generator to select the sample. For example, if we wanted to select a sample of 50 students from a school with 1000 students, we could assign each student a number from 1 to 1000 and use a random number generator to select 50 numbers between 1 and 1000.

Simple random sampling is a popular method of sampling because it is easy to understand and implement. However, it may not always be the most efficient method of sampling. For example, if the population is very large, it may be more efficient to use a stratified sampling method where the population is divided into subgroups and a sample is selected from each subgroup.

To ensure that the sample is representative of the population, it is important to use a large enough sample size. The sample size required will depend on the size of the population and the level of precision required. The formula for calculating the sample size required for a given level of precision is:

n = (z^2 * p * q) / e^2

Where:
n = sample size
z = the z-score for the desired level of confidence (e.g. 1.96 for 95% confidence)
p = the proportion of the population with the characteristic of interest
q = 1 - p
e = the desired level of precision (i.e. the maximum margin of error)

Overall, simple random sampling is a useful method of selecting a sample from a population where each member has an equal chance of being chosen. However, it is important to consider other sampling methods and to use an appropriate sample size to ensure that the sample is representative of the population.