Simple Random Sampling
Simple random sampling is the most widelyused probability sampling method,
probably because it is easy to implement and easy to analyze.
Key Definitions
To understand simple random sampling, you need to first understand a few key definitions.

A random number table is a list of numbers, composed of the
digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Numbers in the list are arranged so
that each digit has no predictable relationship to the digits that preceded it
or to the digits that followed it. In short, the digits are arranged randomly.
The numbers in a random number table are random numbers.
Simple Random Sampling
Simple random sampling refers to a sampling method that has the
following properties.

All possible samples of n objects are equally likely to occur.
An important benefit of simple random sampling is that it allows researchers to use
statistical methods to analyze sample results. For example, given a simple random
sample, researchers can use statistical methods to define a
confidence interval around a sample mean. Statistical
analysis is not appropriate when nonrandom sampling methods are used.
There are many ways to obtain a simple random sample. One way would be the
lottery method. Each of the N population members is assigned a unique
number. The numbers are placed in a bowl and thoroughly mixed. Then, a
blindfolded researcher selects n numbers. Population members having the
selected numbers are included in the sample.
Random Number Generator
In practice, the lottery method described above can be cumbersome, particularly
with large sample sizes. As an alternative, use Stat Trek's Random Number
Generator. With the Random Number Generator, you can select up to random
numbers quickly and easily. This tool is provided at no cost  free!! To access
the Random Number Generator, simply click on the button below.
It can also be found under the Stat Tools
tab, which appears in the header of every Stat Trek web page.
Sampling With Replacement and Without Replacement
Suppose we use the lottery method described above to select a simple random
sample. After we pick a number from the bowl, we can put the number aside or we
can put it back into the bowl. If we put the number back in the bowl, it may be
selected more than once; if we put it aside, it can selected only one time.
When a population element can be selected more than one time, we are sampling
with replacement. When a population element can be selected only
one time, we are sampling without replacement.