Question

A petition with 500 signatures is submitted to a university's student council. The council president would like to determine the proportion of those who signed the petition who are actually registered students at the university. There is not enough time to check all 500 names with the registrar, so the council president decides to select a simple random sample of 30 signatures. Describe how this might be done.

Short answer

To conduct a simple random sample from the 500 petition signees, first create a list of all individuals who signed the petition. Then, generate 30 unique random numbers and select the corresponding individuals from the list. These form the sample of 30 signatures which will be cross-checked with the register.

Step-by-step solution

Understanding Simple Random Sampling

Simple random sampling is a type of probability sampling technique where each member of the given population has an equal opportunity to be chosen as a part of the sample. It's one of the simplest and most basic forms of statistical sampling methods.

Execute Simple Random Sampling

To draw a simple random sample, there needs to be a full list of all 500 individuals who signed the petition. After that, generate a set of random numbers. There are several ways to do this: one method might be to use a random number generator, selecting 30 unique random numbers corresponding to the individuals on the list. Most calculators and statistical software have a function to generate these random numbers.

Sample Selection

Once the random numbers are generated, each number will correlate to an individual in the provided list of petition signees. Those individuals that match the generated random numbers will make up the random sample of 30 signatures. They can then be cross-checked with the register to determine what proportion are registered students at the university.