Random SamplingIs that Random?

A sample is a collection of data from some fraction of a population.

It allows us to learn about the entire population by studying a relatively small portion of the population.

A sample frame is the collection of individuals from which a sample is drawn.

Sample

A census is when every individual in the population is measured.

Not difficult if your population is Mr. Rick’s 7th period.

Imagine your population is all household in the Commonwealth of Virginia.

What would happen by the them you collected data from the entire population?

Would there be some households that could be easily missed?

Census

Suppose you are interested in knowing the mean height for everyone in your school. ◦ What would a census tell you?

◦ How close would a sample size of one less student that the population be to the mean of the population?

◦ What about ten less students?

◦ If you took a sample of 100 and another sample of 10, which mean would be closer to the population?

Census vs. Sample

In general, a larger sample size will result in a more accurate estimate of the population.

When the population is very large, larger samples will not produce significantly better results and are usually more expensive or difficult to obtain.

A balance is usually made, not too small to sacrifice accuracy, and not too large to sacrifice cost.

For very large populations a sample size in the hundreds is normally sufficient.

Census vs. Sample

Making sure that a sample is truly random means that the person taking the sample has no control over who is selected.

When a sample is not random a bias could appear. This means that some individuals are somehow favored over others in the population.

Random

A Simple Random Sample (SRS) is the result of a sampling method that assures every possible sample of the same size has an equal probability of being selected.

Describe a method that would ensure your sample of 5 students from this class will be a simple random sample. Compare and discuss your method with others in the class.

Simple Random Sample

Random Numbers are a primary tool in selecting SRS.

You can get random numbers from your TI-84 calculator.

Books of random numbers have been published. Page 834

Websites exist which provide truly random numbers. http://www.random.org/

Simple Random Sample