2.6 Sampling and Estimation - 2.6 Sampling and Estimation - Sampling and Estimation

Key Concepts

• Population
• Sample
• Sampling Techniques
• Point Estimation
• Confidence Intervals

Population

A population is the entire group of individuals or items that you are interested in studying. For example, if you are studying the average income of all households in a city, the population would be all households in that city.

Sample

A sample is a subset of the population that is selected for study. Instead of studying the entire population, which can be impractical or costly, researchers often study a sample to make inferences about the population. For example, if you select 1,000 households from the city to study, those 1,000 households are your sample.

Sampling Techniques

Sampling techniques are methods used to select a sample from a population. Common techniques include:

• Simple Random Sampling: Each member of the population has an equal chance of being selected.
• Stratified Sampling: The population is divided into subgroups (strata), and random samples are taken from each subgroup.
• Cluster Sampling: The population is divided into clusters, and entire clusters are randomly selected for the sample.

Example: To study the average income of households in a city, you could use stratified sampling by dividing the city into neighborhoods (strata) and selecting a random sample of households from each neighborhood.

Point Estimation

Point estimation involves using a single value, or point, to estimate a population parameter. For example, if you calculate the average income of your sample and use that average as an estimate of the average income of the entire population, that average is a point estimate.

Example: If the average income of the 1,000 households in your sample is $60,000, you might use $60,000 as a point estimate for the average income of all households in the city.

Confidence Intervals

A confidence interval is a range of values that is likely to contain the population parameter with a certain level of confidence. For example, a 95% confidence interval for the average income might be $58,000 to $62,000. This means that you are 95% confident that the true average income of all households in the city falls within this range.

Example: If your sample's average income is $60,000, and you calculate a 95% confidence interval of $58,000 to $62,000, you can say with 95% confidence that the true average income of all households in the city is between $58,000 and $62,000.