Chapter Six Normal Curves and Sampling Probability Distributions

Chapter 6 Section 4 Sampling Distributions

Review of Statistical Terms

Population

Sample A subset of measurements from a population. We use information obtained from a sample to make inferences about the population. For a given population, there is a very large number of possible samples.

A numerical descriptive measure of a population. Parameter A numerical descriptive measure of a population.

Examples of Population Parameters The population mean, denoted by μ, is a population parameter. The population standard deviation, denoted by σ, is a population parameter. The population value in a binomial experiment of the probability of success for one trial, denoted by p, is a population parameter.

Statistic

Examples of Sample Statistics

Sample statistics are used to make inferences about population parameters Statistic are used to estimate the value of a parameter. Statistics are used to make decisions about the value of a parameter. If we were somehow able to produce all the possible samples of the same size, calculate each sample mean, and then observe the resulting distribution, we would be examining what is called the sampling distribution. When we are interested in investigating a population mean, we must know about the sampling distribution for sample means of a given sample size.

Principal types of inferences Estimation: In this type of inference, we estimate the value of a population parameter. Testing: In this type of inference, we formulate a decision about the value of a population parameter. Regression: In this type of inference, we make predictions or forecasts about the value of a statistical variable.

Sampling distribution A sampling distribution is a probability distribution of a sample statistic based on all possible simple random samples of the same size from the same population.

END OF SECTION 4