Chapter Six Normal Curves and Sampling Probability Distributions

1. Chapter SixNormal Curves and Sampling Probability Distributions

2. Chapter 6Section 4Sampling Distributions

3. Review of Statistical Terms

4. Population

5. 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.

6. Parameter A numerical descriptive measure of a population.

7. 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.

9. Statistic

10. Examples of Sample Statistics

11. 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.

12. 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.

13. 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.

14. ENDOFSECTION 4